Chapter 4

How much is the work done in pulling up a block of wood weighing \(2 \mathrm{KN}\) for a length of \(10 \mathrm{~m}\) on a smooth plane inclined at an angle of \(30^{\circ}\) with the horizontal? (A) \(1.732 \mathrm{KJ}\) (B) \(17.32 \mathrm{KJ}\) (C) \(10 \mathrm{KJ}\) (D) \(100 \mathrm{KJ}\)

A force of \(7 \mathrm{~N}\), making an angle \(\theta\) with the horizontal, acting on an object displaces it by \(0.5 \mathrm{~m}\) along the horizontal direction. If the object gains K.E. of \(2 \mathrm{~J}\), what is the horizontal component of the force? (A) \(2 \mathrm{~N}\) (B) \(4 \mathrm{~N}\) (C) \(1 \mathrm{~N}\) (D) \(14 \mathrm{~N}\)

A \(60 \mathrm{~kg}\) JATAN with \(10 \mathrm{~kg}\) load on his head climbs 25 steps of \(0.20 \mathrm{~m}\) height each. What is the work done in climbing ? \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(5 \mathrm{~J}\) (B) \(350 \mathrm{~J}\) (C) \(100 \mathrm{~J}\) (D) \(3500 \mathrm{~J}\)

A ball of mass \(5 \mathrm{~kg}\) is striding on a plane with initial velocity of \(10 \mathrm{~m} / \mathrm{s}\). If co-efficient of friction between surface and ball is \((1 / 2)\), then before stopping it will describe \(\ldots \ldots\) \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(12.5 \mathrm{~m}\) (B) \(5 \mathrm{~m}\) (C) \(7.5 \mathrm{~m}\) (D) \(10 \mathrm{~m}\)

The force constant of a wire is \(\mathrm{K}\) and that of the another wire is \(3 \mathrm{k}\) when both the wires are stretched through same distance, if work done are \(\mathrm{W}_{1}\) and \(\mathrm{W}_{2}\), then... (A) \(\mathrm{w}_{2}=3 \mathrm{w}_{1}^{2}\) (B) \(\mathrm{W}_{2}=0.33 \mathrm{~W}_{1}\) (C) \(\mathrm{W}_{2}=\mathrm{W}_{1}\) (D) \(\mathrm{W}_{2}=3 \mathrm{~W}_{1}\)

A spring of spring constant \(10^{3} \mathrm{~N} / \mathrm{m}\) is stretched initially \(4 \mathrm{~cm}\) from the unscratched position. How much the work required to stretched it further by another \(5 \mathrm{~cm}\) ? (A) \(6.5 \mathrm{NM}\) (B) \(2.5 \mathrm{NM}\) (C) \(3.25 \mathrm{NM}\) (D) \(6.75 \mathrm{NM}\)

The mass of a car is \(1000 \mathrm{~kg}\). How much work is required to be done on it to make it move with a speed of \(36 \mathrm{~km} / \mathrm{h}\) ? (A) \(2.5 \times 10^{4} \mathrm{~J}\) (B) \(5 \times 10^{3} \mathrm{~J}\) (C) \(500 \mathrm{~J}\) (D) \(5 \times 10^{4} \mathrm{~J}\)

A body of mass \(6 \mathrm{~kg}\) is under a force, which causes a displacement in it given by \(\mathrm{S}=\left[\left(2 \mathrm{t}^{3}\right) / 3\right](\mathrm{in} \mathrm{m}) .\) Find the work done by the force in first one seconds. (A) \(2 \mathrm{~J}\) (B) \(3.8 \mathrm{~J}\) (C) \(5.2 \mathrm{~J}\) (D) \(24 \mathrm{~J}\)

A spring gun of spring constant \(90 \times 10^{2} \mathrm{~N} / \mathrm{M}\) is compressed \(4 \mathrm{~cm}\) by a ball of mass \(16 \mathrm{~g}\). If the trigger is pulled, calculate the velocity of the ball. (A) \(60 \mathrm{~m} / \mathrm{s}\) (B) \(3 \mathrm{~m} / \mathrm{s}\) (C) \(90 \mathrm{~m} / \mathrm{s}\) (D) \(30 \mathrm{~m} / \mathrm{s}\)

A uniform chain of length \(2 \mathrm{~m}\) is kept on a table such that a length of \(50 \mathrm{~cm}\) hangs freely from the edge of the table. The total mass of the chain is \(5 \mathrm{~kg}\). What is the work done in pulling the entire chain on the table. \(\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{2}\right)\) (A) \(7.2 \mathrm{~J}\) (B) \(3 \mathrm{~J}\) (C) \(4.6 \mathrm{~J}\) (D) \(120 \mathrm{~J}\)

A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one third of its is hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on to the table is (A) MgL (B) \([(\mathrm{MgL}) /(3)]\) (C) \([(\mathrm{MgL}) /(9)]\) (D) \([(\mathrm{MgL}) /(18)]\)

A cord is used to lower vertically a block of mass \(\mathrm{M}\) by a distance \(\mathrm{d}\) with constant downward acceleration \((9 / 2)\). Work done by the cord on the block is (A) \(-\mathrm{Mgd} / 2\) (B) \(\mathrm{Mgd} / 4\) (C) \(-3 \mathrm{Mgd} / 4\) (D) \(\mathrm{Mgd}\)

Natural length of a spring is \(60 \mathrm{~cm}\), and its spring constant is \(2000 \mathrm{~N} / \mathrm{m}\). A mass of \(20 \mathrm{~kg}\) is hung from it. The extension produced in the spring is..... \(\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(4.9 \mathrm{~cm}\) (B) \(0.49 \mathrm{~cm}\) (C) \(9.8 \mathrm{~cm}\) (D) \(0.98 \mathrm{~cm}\)

The potential energy of a body is given by \(\mathrm{U}=\mathrm{A}-\mathrm{Bx}^{2}\) (where \(\mathrm{x}\) is displacement). The magnitude of force acting on the particle is (A) constant (B) proportional to \(\mathrm{x}\) (C) proportional to \(\mathrm{x}^{2}\) (D) Inversely proportional to \(\mathrm{x}\)

A uniform chain of length \(\mathrm{L}\) and mass \(\mathrm{M}\) is lying on a smooth table and \((1 / 4)^{\text {th }}\) of its length is hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on to the table is (A) MgL (B) \(\mathrm{MgL} / 9\) (C) \(\mathrm{MgL} / 18\) (D) \(\mathrm{MgL} / 32\)

If Wa, Wb, and Wc represent the work done in moving a particle from \(\mathrm{X}\) to \(\mathrm{Y}\) along three different path \(\mathrm{a}, \mathrm{b}\), and \(\mathrm{c}\) respectively (as shown) in the gravitational field of a point mass \(\mathrm{m}\), find the correct relation between \(\mathrm{Wa}, \mathrm{Wb}\) and \(\mathrm{Wc}\) (A) \(\mathrm{Wb}>\mathrm{Wa}>\mathrm{Wc}\) (B) \(\mathrm{Wa}<\mathrm{Wb}<\mathrm{Wc}\) (C) \(\mathrm{Wa}>\mathrm{Wb}>\mathrm{Wc}\) (D) \(\mathrm{Wa}=\mathrm{Wb}=\mathrm{Wc}\)

An open knife edge of mass \(\mathrm{m}\) is dropped from a height \(\mathrm{h}\) on a wooden floor. If the blade penetrates up to the depth d into the wood, the average resistance offered by the wood to the knife edge is, (A) \(\mathrm{mg}\) (B) \(\mathrm{mg}(1+\\{\mathrm{h} / \mathrm{d}\\})\) (C) \(\mathrm{mg}(1+\\{\mathrm{h} / \mathrm{d}\\})^{2}\) (D) \(m g(1-\\{h / d\\})\)

A particle of mass \(0.5 \mathrm{~kg}\) travels in a straight line with velocity \(\mathrm{v}=\mathrm{ax}^{3 / 2}\), Where \(\mathrm{a}=5 \mathrm{~m}^{[(-1) / 2]} \mathrm{s}^{-1}\). The work done by the net force during its displacement from \(\mathrm{x}=0\) to \(\mathrm{x}=2 \mathrm{~m}\) is (A) \(50 \mathrm{~J}\) (B) \(45 \mathrm{~J}\) (C) \(25 \mathrm{~J}\) (D) None of these

A mass of \(\mathrm{M} \mathrm{kg}\) is suspended by a weight-less string, the horizontal force that is required to displace it until the string makes an angle of \(60^{\circ}\) with the initial vertical direction is (A) \(\mathrm{Mg} / \sqrt{3}\) (B) \(\mathrm{Mg} \cdot \sqrt{2}\) (C) \(\mathrm{Mg} / \sqrt{2}\) (D) \(\mathrm{Mg} \cdot \sqrt{3}\)

A force \(F=A y^{2}+B y+C\) acts on a body in the \(y\) -direction. The work done by this force during a displacement from \(\mathrm{y}=-\mathrm{a}\) to \(\mathrm{y}=\mathrm{a}\) is (A) \(\left[\left\\{2 \mathrm{Aa}^{3}\right\\} / 3\right]\) (B) \(\left[\left\\{2 \mathrm{Aa}^{3}\right\\} / 3\right]+2 \mathrm{ca}\) (C) \(\left[\left\\{2 \mathrm{Aa}^{3}\right\\} / 3\right]+\left[\left\\{\mathrm{Ba}^{2}\right\\} / 2\right]+\mathrm{ca}\) (D) None of these.

A spring with spring constant \(\mathrm{K}\) when stretched through \(2 \mathrm{~cm}\) the potential energy is \(\mathrm{U}\). If it is stretched by \(6 \mathrm{~cm}\). The potential energy will be...... (A) \(6 \mathrm{U}\) (B) \(3 \mathrm{U}\) (C) \(9 \mathrm{U}\) (D) \(18 \mathrm{U}\)

If linear momentum of body is increased by \(1.5 \%\), its kinetic energy increases by...... \(\%\) (A) \(0 \%\) (B) \(10 \%\) (C) \(2.25 \%\) (D) \(3 \%\)

With what velocity should a student of mass \(40 \mathrm{~kg}\) run so that his kinetic energy becomes \(160 \mathrm{~J}\) ? (A) \(4 \mathrm{~m} / \mathrm{s}\) (B) \(\sqrt{8} \mathrm{~m} / \mathrm{s}\) (C) \(16 \mathrm{~m} / \mathrm{s}\) (D) \(8 \mathrm{~m} / \mathrm{s}\)

A body of mass \(1 \mathrm{~kg}\) is thrown upwards with a velocity \(20 \mathrm{~m} / \mathrm{s}\). It momentarily comes to rest after a height \(18 \mathrm{~m}\). How much energy is lost due to air friction. \((\mathrm{g}=10 \mathrm{~m} / \mathrm{s} 2)\) (A) \(20 \mathrm{~J}\) (B) \(30 \mathrm{~J}\) (C) \(40 \mathrm{~J}\) (D) \(10 \mathrm{~J}\)

Two bodies of masses \(m_{1}\) and \(m_{2}\) have equal kinetic energies. If \(P_{1}\) and \(P_{2}\) are their respective momentum, what is ratio of \(\mathrm{P}_{2}: \mathrm{P}_{1}\) ? (A) \(\mathrm{m}_{1}: \mathrm{m}_{2}\) (B) \(\sqrt{\mathrm{m}}_{2} / \sqrt{\mathrm{m}_{1}}\) (C) \(\sqrt{m_{1}}: \sqrt{m_{2}}\) (D) \(\mathrm{m}_{1}^{2}: \mathrm{m}_{2}^{2}\)

A body having a mass of \(0.5 \mathrm{~kg}\) slips along the wall of a semispherical smooth surface of radius \(20 \mathrm{~cm}\) shown in figure. What is the velocity of body at the bottom of the surface \(?\left(\mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(2 \mathrm{~m} / \mathrm{s}\) (B) \(2 \mathrm{~m} / \mathrm{s}\) (C) \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\) (D) \(4 \mathrm{~m} / \mathrm{s}\)

Two bodies of masses \(\mathrm{m}\) and \(3 \mathrm{~m}\) have same momentum. their respective kinetic energies \(E_{1}\) and \(E_{2}\) are in the ratio..... (A) \(1: 3\) (B) \(3: 1\) (C) \(1: 3\) (D) \(1: 6\)

What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of \(18 \mathrm{~cm}\) (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) ) (A) \(0.4 \mathrm{~m} / \mathrm{s}\) (B) \(4 \mathrm{~m} / \mathrm{s}\) (C) \(1.8 \mathrm{~m} / \mathrm{s}\) (D) \(0.6 \mathrm{~m} / \mathrm{s}\)

A spring is compressed by \(1 \mathrm{~cm}\) by a force of \(4 \mathrm{~N}\). Find the potential energy of the spring when it is compressed by \(10 \mathrm{~cm}\) (A) \(2 \mathrm{~J}\) (B) \(0.2 \mathrm{~J}\) (C) \(20 \mathrm{~J}\) (D) \(200 \mathrm{~J}\)

When \(2 \mathrm{~kg}\) mass hangs to a spring of length \(50 \mathrm{~cm}\), the spring stretches by \(2 \mathrm{~cm}\). The mass is pulled down until the length of the spring becomes \(60 \mathrm{~cm}\). What is the amount of elastic energy stored in the spring in this condition, if \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) (A) \(10 \mathrm{~J}\) (B) \(2 \mathrm{~J}\) (C) \(2.5 \mathrm{~J}\) (D) \(5 \mathrm{~J}\)

The potential energy of a projectile at its highest point is (1/2) th the value of its initial kinetic energy. Therefore its angle of projection is (A) \(30^{\circ}\) (B) \(45^{\circ}\) (C) \(60^{\circ}\) (D) \(75^{\circ}\)

Two bodies \(\mathrm{P}\) and \(\mathrm{Q}\) have masses \(5 \mathrm{~kg}\) and \(20 \mathrm{~kg}\) respectively. Each one is acted upon by a force of \(4 \mathrm{~N}\). If they acquire the same kinetic energy in times \(t_{\mathrm{P}}\) and \(\mathrm{t}_{\mathrm{Q}}\) then the ratio \(\left(t_{q} / t_{p}\right)=\ldots \ldots\) \((\mathrm{A})(1 / 2)\) (B) 2 (C) 5 (D) 6

A particle of mass \(0.1 \mathrm{~kg}\) is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at \(\mathrm{x}=0\). What is the particle's velocity square at \(\mathrm{x}=6 \mathrm{~cm}\) ? (A) \(0(\mathrm{~m} / \mathrm{s})^{2}\) (B) \(240 \sqrt{2}(\mathrm{~m} / \mathrm{s})^{2}\) (C) \(240 \sqrt{3}(\mathrm{~m} / \mathrm{s})^{2}\) (D) \(480(\mathrm{~m} / \mathrm{s})^{2}\)

The potential energy of \(2 \mathrm{~kg}\) particle, free to move along \(\mathrm{x}\) axis is given by \(\mathrm{U}(\mathrm{X})=\left[\left\\{\mathrm{x}^{4} / 4\right\\}-\left\\{\mathrm{x}^{2} / 2\right\\}\right] \mathrm{J}\). If its mechanical energy is \(2 \mathrm{~J}\), its maximum speed is \(\ldots \mathrm{m} / \mathrm{s}\) (A) \((3 / 2)\) (B) \(\sqrt{2}\) (C) \((1 / \sqrt{2})\) (D) 2

If the K.E. of a body is increased by \(44 \%\), its momentum will increase by....... (A) \(20 \%\) (B) \(22 \%\) (C) \(2 \%\) (D) \(120 \%\)

A bullet of mass \(0.10 \mathrm{~kg}\) moving with a speed of \(100 \mathrm{~m} / \mathrm{s}\) enters a wooden block and is stopped after a distance of \(0.20 \mathrm{~m}\). What is the average resistive force exerted by the block on the bullet ? (A) \(2.5 \times 10^{2} \mathrm{~N}\) (B) \(25 \mathrm{~N}\) (C) \(25 \times 10^{2} \mathrm{~N}\) (D) \(2.5 \times 10^{4} \mathrm{~N}\)

A rifle bullet loses \((1 / 10)^{\text {th }}\) of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is (A) 5 (B) 10 (C) 11 (D) 20

A sphere of mass \(\mathrm{m}\) moving the velocity \(\mathrm{v}\) enters a hanging bag of sand and stops. If the mass of the bag is \(\mathrm{M}\) and it is raised by height \(\mathrm{h}\), then the velocity of the sphere was (A) \([\\{\mathrm{m}+\mathrm{M}\\} / \mathrm{m}] \sqrt{(2 \mathrm{gh})}\) (B) \((\mathrm{M} / \mathrm{m}) \sqrt{(} 2 \mathrm{gh})\) (C) \([\mathrm{m} /\\{\mathrm{M}+\mathrm{m}\\}] \sqrt{(2 \mathrm{gh})}\) (D) \((\mathrm{m} / \mathrm{M}) \sqrt{(2 \mathrm{gh})}\)

A particle is acted upon by a force \(\mathrm{F}\) which varies with position \(\mathrm{x}\) as shown in figure. If the particle at \(\mathrm{x}=0\) has kinetic energy of \(20 \mathrm{~J}\). Then the calculate the kinetic energy of the particle at \(\mathrm{x}=16 \mathrm{~cm}\). (A) \(45 \mathrm{~J}\) (B) \(30 \mathrm{~J}\) (C) \(70 \mathrm{~J}\) (D) \(135 \mathrm{~J}\)

If the water falls from a dam into a turbine wheel \(19.6 \mathrm{~m}\) below, then the velocity of water at the turbine is \(\ldots \ldots\) \(\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(9.8 \mathrm{~m} / \mathrm{s}\) (B) \(19.6 \mathrm{~m} / \mathrm{s}\) (C) \(39.2 \mathrm{~m} / \mathrm{s}\) (D) \(98.0 \mathrm{~m} / \mathrm{s}\)

A bomb of \(12 \mathrm{~kg}\) divides in two parts whose ratio of masses is \(1: 4 .\) If kinetic energy of smaller part is \(288 \mathrm{~J}\), then momentum of bigger part in \(\mathrm{kgm} / \mathrm{sec}\) will be (A) 38 (B) 72 (C) 108 (D) Data is incomplete

An ice-cream has a marked value of \(700 \mathrm{kcal}\). How many kilo-watt- hour of energy will it deliver to the body as it is digested \((\mathrm{J}=4.2 \mathrm{~J} / \mathrm{cal})\) (A) \(0.81 \mathrm{kwh}\) (B) \(0.90 \mathrm{kwh}\) (C) \(1.11 \mathrm{kwh}\) (D) \(0.71 \mathrm{kwh}\)

A spherical ball of mass \(15 \mathrm{~kg}\) stationary at the top of a hill of height \(82 \mathrm{~m} .\) It slides down a smooth surface to the ground, then climbs up another hill of height \(32 \mathrm{~m}\) and finally slides down to horizontal base at a height of \(10 \mathrm{~m}\) above the ground. The velocity attained by the ball is (A) \(30 \sqrt{10 \mathrm{~m} / \mathrm{s}}\) (B) \(10 \sqrt{30 \mathrm{~m} / \mathrm{s}}\) (C) \(12 \sqrt{10} \mathrm{~m} / \mathrm{s}\) (D) \(10 \sqrt{12} \mathrm{~m} / \mathrm{s}\)

A bomb of mass \(10 \mathrm{~kg}\) explodes into 2 pieces of mass \(4 \mathrm{~kg}\) and \(6 \mathrm{~kg}\). The velocity of mass \(4 \mathrm{~kg}\) is \(1.5 \mathrm{~m} / \mathrm{s}\), the K.E. of mass \(6 \mathrm{~kg}\) is ....... (A) \(3.84 \mathrm{~J}\) (B) \(9.6 \mathrm{~J}\) (C) \(3.00 \mathrm{~J}\) (D) \(2.5 \mathrm{~J}\)

A bomb of mass \(3.0 \mathrm{~kg}\) explodes in air into two pieces of masses \(2.0 \mathrm{~kg}\) and \(1.0 \mathrm{~kg}\). The smaller mass goes at a speed of \(80 \mathrm{~m} / \mathrm{s}\). The total energy imparted to the two fragments is (A) \(1.07 \mathrm{KJ}\) (B) \(2.14 \mathrm{KJ}\) (C) \(2.4 \mathrm{KJ}\) (D) \(4.8 \mathrm{KJ}\)

The bob of simple pendulum (mass \(\mathrm{m}\) and length 1 ) dropped from a horizontal position strike a block of the same mass elastically placed on a horizontal frictionless table. The K.E. of the block will be (A) \(2 \mathrm{mg} 1\) (B) \(\mathrm{mg} 1 / 2\) (C) \(\mathrm{mg} 1\) (D) zero

A gun fires a bullet of mass \(40 \mathrm{~g}\) with a velocity of \(50 \mathrm{~m} / \mathrm{s}\). Because of this the gun is pushed back with a velocity of \(1 \mathrm{~m} / \mathrm{s}\). The mass of the gun is (A) \(1.5 \mathrm{~kg}\) (B) \(3 \mathrm{~kg}\) (C) \(2 \mathrm{~kg}\) (D) \(2.5 \mathrm{~kg}\)

The decreases in the potential energy of a ball of mass \(25 \mathrm{~kg}\) which falls from a height of \(40 \mathrm{~cm}\) is (A) \(968 \mathrm{~J}\) (B) \(100 \mathrm{~J}\) (C) \(1980 \mathrm{~J}\) (D) \(200 \mathrm{~J}\)

If a man increase his speed by \(2 \mathrm{~m} / \mathrm{s}\), his \(\mathrm{K} . \mathrm{E}\). is doubled, the original speed of the man is (A) \((2+2 \sqrt{2}) \mathrm{m} / \mathrm{s}\) (B) \((2+\sqrt{2}) \mathrm{m} / \mathrm{s}\) (C) \(4 \mathrm{~m} / \mathrm{s}\) (D) \((1+2 \sqrt{2}) \mathrm{m} / \mathrm{s}\)

A nucleus at rest splits into two nuclear parts having same density and radii in the ratio \(1: 2\). Their velocities are in the ratio (A) \(2: 1\) (B) \(4: 1\) (C) \(6: 1\) (D) \(8: 1\)