Chapter 3

The velocity of a body of mass \(20 \mathrm{~kg}\) decrease from \(20 \mathrm{~ms}^{-1}\) to \(5 \mathrm{~ms}^{-1}\) in a distance of \(100 \mathrm{~m}\). Force on the body is (A) \(-27.5 \mathrm{~N}\) (B) \(-47.5 \mathrm{~N}\) (C) \(-37.5 \mathrm{~N}\) (D) \(-67.5 \mathrm{~N}\)

A ball of mass \(0.2 \mathrm{~kg}\) is thrown vertically upwards by applying a force by hand. if the hand moves \(0.2 \mathrm{~m}\) while applying the force and the ball goes up to \(2 \mathrm{~m}\) height further. find the magnitude of the force. (Consider \(\mathrm{g}=10 \mathrm{~ms}^{-1}\) ) (A) \(16 \mathrm{~N}\) (B) \(20 \mathrm{~N}\) (C) \(22 \mathrm{~N}\) (D) \(4 \mathrm{~N}\)

Formula for true force is (A) \(\mathrm{F}=\mathrm{ma}\) (B) \(\mathrm{F}=[\\{\mathrm{d}(\mathrm{mv})\\} / \mathrm{dt}]\) (C) \(\mathrm{F}=\mathrm{m}(\mathrm{dv} / \mathrm{dt})\) (D) \(F=m\left(d^{2} x / d t^{2}\right)\)

A Particle moves in the X-Y plane under the influence of a force such that its linear momentum is \(\mathrm{P}^{-}(\mathrm{t})=\mathrm{A}[\mathrm{i} \cos (\mathrm{kt})-\mathrm{j} \sin (\mathrm{kt})]\) where \(\mathrm{A}\) and \(\mathrm{k}\) are constants. The angle between the force and momentum is (A) \(0^{\circ}\) (B) \(30^{\circ}\) (C) \(45^{\circ}\) (D) \(90^{\circ}\)

Force of \(5 \mathrm{~N}\) acts on a body of weight \(9.8 \mathrm{~N}\). what is the acceleration produced in \(\mathrm{ms}^{-2}\). (A) \(49.00\) (B) \(5.00\) (C) \(1.46\) (D) \(0.51\)

Same force acts on two bodies of different masses \(2 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) initially at rest. the ratio of times required to acquire same final velocity is (A) \(2: 1\) (B) \(1: 2\) (C) \(1: 1\) (D) \(4: 16\)

10,000 small balls, each weighing \(1 \mathrm{~g}\) strike one square \(\mathrm{cm}\) of area per second with a velocity \(100 \mathrm{~ms}^{-1}\) in a normal direction and rebound with the same velocity. The value of pressure on the surface will be (A) \(2 \times 10^{3} \mathrm{Nm}^{-2}\) (B) \(2 \times 10^{5} \mathrm{Nm}^{-2}\) (C) \(10^{7} \mathrm{Nm}^{-2}\) (D) \(2 \times 10^{7} \mathrm{Nm}^{2}\)

A player caught a cricket ball of mass \(150 \mathrm{~g}\) moving at the rate of \(20 \mathrm{~ms}^{-1}\). If the catching process be completed in \(0.1 \mathrm{~s}\) the force of the blow exerted by the ball on the hands of player is (A) \(0.3 \mathrm{~N}\) (B) \(30 \mathrm{~N}\) (C) \(300 \mathrm{~N}\) (D) \(3000 \mathrm{~N}\)

A body of mass \(5 \mathrm{~kg}\) starts from the origin with an initial velocity \(u^{\rightarrow}=30 \mathrm{i}+40 \mathrm{j} \mathrm{ms}^{-1}\). If a constant Force \(\underline{F}=-\left(\mathrm{i}^{\wedge}+5 \mathrm{j}\right) \mathrm{N}\) acts on the body, the time in which the y-component of the velocity becomes zero is (A) \(5 \mathrm{~s}\) (B) \(20 \mathrm{~s}\) (C) \(40 \mathrm{~s}\) (D) \(80 \mathrm{~s}\)

Swimming is possible on account of (A) First law of motion (B) second law of motion (C) Third law of motion (D) Newton's law of gravitation

A cold soft drink is kept on the balance. When the cap is open, then the weight (A) Increases (B) Decreases (C) First increase then decreases (D) Remains same

A wagon weighing \(1000 \mathrm{~kg}\) is moving with a velocity \(50 \mathrm{~km} \mathrm{~h}^{-1}\) on smooth horizontal rails. A mass of \(250 \mathrm{~kg}\) is dropped into it. The velocity with which it moves now is (A) \(2.5 \mathrm{~km} \mathrm{~h}^{-1}\) (B) \(20 \mathrm{~km} \mathrm{~h}^{-1}\) (C) \(40 \mathrm{~km} \mathrm{~h}^{-1}\) (D) \(50 \mathrm{~km} \mathrm{~h}^{-1}\)

Three Forces \(F_{1}, F_{2}\), and \(F_{3}\) together keep a body in equilibrium. If \(F_{1}=3 \mathrm{~N}\) along the positive \(\mathrm{X}\) - axis, \(\mathrm{F}_{2}=4 \mathrm{~N}\) along the positive Y-axis then the third force \(F_{3}\) is (A) \(5 \mathrm{~N}\) -making an angle \(\theta=\tan ^{-1}(3 / 4)\) with negative \(\mathrm{y}\) -axis (B) \(5 \mathrm{~N}\) -making an angle \(\theta=\tan ^{-1}(4 / 3)\) with negative \(\mathrm{y}\) -axis (C) \(7 \mathrm{~N}\) -making an angle \(\theta=\tan ^{-1}(3 / 4)\) with negative \(\mathrm{y}\) -axis (D) \(7 \mathrm{~N}\) -making an angle \(\theta=\tan ^{-1}(4 / 3)\) with negative \(\mathrm{y}\) -axis

A block of mass \(4 \mathrm{~kg}\) is placed on a rough horizontal plane. A time dependent force \(\mathrm{F}=\mathrm{Kt}^{2}\) acts on a block, where \(\mathrm{k}=2 \mathrm{~N} / \mathrm{s}^{2}\), co-efficient of friction \(\mu=0.8\). Force of friction between the block and the plane at \(\mathrm{t}=2 \mathrm{~S}\) is.... (A) \(32 \mathrm{~N}\) (B) \(4 \mathrm{~N}\) (C) \(2 \mathrm{~N}\) (D) \(8 \mathrm{~N}\)

A \(7 \mathrm{~kg}\) object is subjected to two forces (in newton) \(\underline{F}_{1}=20 \mathrm{i}^{-}+30 \mathrm{j}^{-}\) and \(\underline{\mathrm{F}}_{2}=8 \mathrm{i}^{-}-5 \mathrm{j}\) `The magnitude of resulting acceleration in \(\mathrm{ms}^{-2}\) will be (A) 5 (B) 4 (C) 3 (D) 2

A car travelling at a speed of \(30 \mathrm{~km} / \mathrm{h}\) is brought to a halt in 8 meters by applying brakes. If the same car is travelling at \(60 \mathrm{~km} / \mathrm{h}\) it can be brought to a halt with the same breaking power in (A) \(8 \mathrm{~m}\) (B) \(16 \mathrm{~m}\) (C) \(24 \mathrm{~m}\) (D) \(32 \mathrm{~m}\)

A given object takes n times more time to slide down \(45^{\circ}\) rough inclined plane as it takes to slide down a perfectly smooth \(45^{\circ}\) incline. The coefficient of kinetic friction between the object and the incline is (A) \(\left[1 /\left(2-\mathrm{n}^{2}\right)\right]\) (B) \(\left[1-\left(1 / \mathrm{n}^{2}\right)\right]\)

Two bodies of equal masses revolve in circular orbits of radii \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2}\) with the same period Their centripetal forces are in the ratio. (A) \(\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)^{2}\) (B) \(\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)\) (C) \(\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{2}\) (D) \(\left.\sqrt{(}_{1} R_{2}\right)\)

Two masses \(\mathrm{M}\) and \((\mathrm{M} / 2)\) are joined together by means of light inextensible string passed over a frictionless pulley as shown in fig. When the bigger mass is released, the small one will ascend with an acceleration (A) \((\mathrm{g} / 3)\) (B) \((3 \mathrm{~g} / 2)\) (C) \(\mathrm{g}\) (D) \((\mathrm{g} / 2)\)

A \(0.5 \mathrm{~kg}\) ball moving with a speed of \(12 \mathrm{~ms}^{-1}\) strikes a hard wall at an angle of \(30^{\circ}\) with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for \(0.25 \mathrm{~S}\) the average force acting on the wall is (A) \(96 \mathrm{~N}\) (B) \(48 \mathrm{~N}\) (C) \(24 \mathrm{~N}\) (D) \(12 \mathrm{~N}\)

A shell of mass \(200 \mathrm{~g}\) is ejected from a gun of mass \(4 \mathrm{~kg}\) by an explosion that generates \(1.05 \mathrm{KJ}\) of energy. The initial velocity of the shell is (A) \(100 \mathrm{~m} / \mathrm{s}\) (B) \(80 \mathrm{~ms}^{-1}\) (C) \(40 \mathrm{~ms}^{-1}\) (D) \(120 \mathrm{~ms}^{-1}\)

A stone of mass \(2 \mathrm{~kg}\) is tied to a string of length \(0.5 \mathrm{~m}\) It the breaking tension of the string is \(900 \mathrm{~N}\), then the maximum angular velocity the stone can have in uniform circular motion is (A) \(30 \mathrm{rad} / \mathrm{s}\) (B) \(20 \mathrm{rad} / \mathrm{s}\) (C) \(10 \mathrm{rad} / \mathrm{s}\) (D) \(25 \mathrm{rad} / \mathrm{s}\)

A sparrow flying in air sits on a stretched telegraph wire. If the weight of the sparrow is \(\mathrm{W}\), which of the following is true about the tension T produced in the wire? (A) \(\mathrm{T}=\mathrm{W}\) (B) \(\mathrm{T}<\mathrm{W}\) (C) \(\mathrm{T}=0\) (D) \(\mathrm{T}>\mathrm{W}\)

A body of mass \(0.05 \mathrm{~kg}\) is falling with acceleration \(9.4 \mathrm{~ms}^{-2}\). The force exerted by air opposite to motion is \(\mathrm{N}\) \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\) (A) \(0.02\) (B) \(0.20\) (C) \(0.030\) (D) Zero

The average force necessary to stop a hammer with 25 NS momentum in \(0.04 \mathrm{sec}\) is \(\quad \mathrm{N}\) (A) 625 (B) 125 (C) 50 (D) 25

Newton's third law of motion leads to the law of conservation of (A) Angular momentum (B) Energy (C) mass (D) momentum

A ball falls on surface from \(10 \mathrm{~m}\) height and rebounds to \(2.5 \mathrm{~m} .\) If duration of contact with floor is \(0.01 \mathrm{sec}\). then average acceleration during contact is \(\mathrm{ms}^{-2}\) (A) 2100 (B) 1400 \(\begin{array}{ll}\text { (C) } 700 & \text { (D) } 400\end{array}\)

A vehicle of \(100 \mathrm{~kg}\) is moving with a velocity of \(5(\mathrm{~m} / \mathrm{s})\). To stop it in \((1 / 10) \mathrm{sec}\), the required force in opposite direction is \(\mathrm{N}\) (A) 50 (B) 500 (C) 5000 (D) 1000

The linear momentum \(\mathrm{P}\) of a particle varies with the time as follows. \(P=a+b t^{2}\) Where \(a\) and \(b\) are constants. The net force acting on the particle is (A) Proportional to t (B) Proportional to t \(^{2}\) (C) Zero (D) constant

which of the following statement is correct? (A) A body has a constant velocity but a varying speed. (B) A body has a constant speed but a varying value of acceleration. (C) A body has a constant speed and zero acceleration. (D) A body has a constant speed but velocity is zero.

A force of \(8 \mathrm{~N}\) acts on an object of mass \(5 \mathrm{~kg}\) in \(\mathrm{X}\) -direction and another force of \(6 \mathrm{~N}\) acts on it in \(\mathrm{Y}\) -direction. Hence, the magnitude of acceleration of object will be (A) \(1.5 \mathrm{~ms}^{-2}\) (B) \(2.0 \mathrm{~ms}^{-2}\) (C) \(2.5 \mathrm{~ms}^{-2}\) (D) \(3.5 \mathrm{~ms}^{-2}\)

A plate of mass \(\mathrm{M}\) is placed on a horizontal frictionless surface and a body of mass \(m\) is placed on this plate, The coefficient of dynamic friction between this body and the plate is \(\mu\). If a force \(2 \mu \mathrm{mg}\). is applied to the body of mass \(\mathrm{m}\) along the horizontal direction the acceleration of the plate will be (A) \((\mu \mathrm{m} / \mathrm{M}) \mathrm{g}\) (B) \([\mu \mathrm{m} /(\mathrm{M}+\mathrm{m})] \mathrm{g}\) (C) \([(2 \mu \mathrm{m}) / \mathrm{M}] \mathrm{g}\) (D) \([(2 \mu \mathrm{m}) /(\mathrm{M}+\mathrm{m})] \mathrm{g}\)

On the horizontal surface of a truck \((=0.6)\), a block of mass \(1 \mathrm{~kg}\) is placed. If the truck is accelerating at the rate of \(5 \mathrm{~m} / \mathrm{s}^{2}\) then frictional force on the block will be \(\mathrm{N}\) (A) 5 (B) 6 (C) \(5.88\) (D) 8

Two blocks of mass \(8 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected a heavy string Placed on rough horizontal Plane, The \(4 \mathrm{~kg}\) block is Pulled with a constant force \(\mathrm{F}\). The co-efficient of friction between the blocks and the ground is \(0.5\), what is the value of \(F\), So that the tension in the spring is constant throughout during the motion of the blocks? \(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\) (A) \(40 \mathrm{~N}\) (B) \(60 \mathrm{~N}\) (C) \(50 \mathrm{~N}\) (D) \(30 \mathrm{~N}\)

A man is standing on a spring balance. Reading of spring balance is \(60 \mathrm{~kg} \mathrm{f}\). If man jumps outside balance, then reading of spring balance (A) First increase than decreases to zero (B) Decreases (C) Increases (D) Remains same

A car turns a corner on a slippery road at a constant speed of \(10 \mathrm{~m} / \mathrm{s}\). If the coefficient of friction is \(0.5\), the minimum radius of the arc at which the car turns is meter. (A) 20 (B) 10 (C) 5 (D) 4

A lift of mass \(1000 \mathrm{~kg}\) is moving with an acceleration of \(1 \mathrm{~ms}^{-2}\) in upward direction Tension developed in the rope of lift is \(\mathrm{N}\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)\) (A) 9800 (B) 10,000 (C) 10,800 (D) 11,000

A rope which can withstand a maximum tension of \(400 \mathrm{~N}\) hangs from a tree. If a monkey of mass \(30 \mathrm{~kg}\) climbs on the rope in which of the following cases-will the rope break? (take \(g=10 \mathrm{~ms}^{-}{\underline{\phantom{xx}}}^{2}\) and neglect the mass of rope \()\) (A) When the monkey climbs with constant speed of \(5 \mathrm{~ms}^{-1}\) (B) When the monkey climbs with constant acceleration of \(2 \mathrm{~ms}^{-2}\) (C) When the monkey climbs with constant acceleration of \(5 \mathrm{~ms}^{-2}\) (D) When the monkey climbs with the constant speed of \(12 \mathrm{~ms}^{-1}\)

An object of mass \(3 \mathrm{~kg}\) is moving with a velocity of \(5 \mathrm{~m} / \mathrm{s}\) along a straight path. If a force of \(12 \mathrm{~N}\) is applied for \(3 \mathrm{sec}\) on the object in a perpendicular to its direction of motion. The magnitude of velocity of the particle at the end of \(3 \mathrm{sec}\) is \(\mathrm{m} / \mathrm{s}\). (A) (B) 12 (C) 13 (D) 4

Same forces act on two bodies of different mass \(2 \mathrm{~kg}\) and \(5 \mathrm{~kg}\) initially at rest. The ratio of times required to acquire same final velocity is (A) \(5: 3\) (B) \(25: 4\) (C) \(4: 25\) (D) \(2: 5\)

A body of mass \(5 \mathrm{~kg}\) starts motion form the origin with an initial velocity \(\mathrm{v}_{0} \rightarrow=30 \mathrm{i}+40 \mathrm{j} \mathrm{m} / \mathrm{s}\) If a constant force \(\mathrm{F}=-\left(\mathrm{i}^{\wedge}+5 \mathrm{j}\right) \mathrm{N}\) acts on the body, than the time in which the Y-component of the velocity becomes zero is (A) \(5 \mathrm{~s}\) (B) \(20 \mathrm{~s}\) (C) \(40 \mathrm{~s}\) (D) \(80 \mathrm{~s}\)

A bag of sand of mass \(\mathrm{m}\) is suspended by rope. a bullet of mass \((\mathrm{m} / 30)\) is fired at it with a velocity \(\mathrm{V}\) and gets embedded into it. The velocity of the bag finally is (A) \((31 \mathrm{~V} / 30)\) (B) \((30 \mathrm{~V} / 31)\) (C) \((\mathrm{V} / 31)\) (D) \((\mathrm{V} / 30)\)

A car of mass \(1000 \mathrm{~kg}\) travelling at \(32 \mathrm{~m} / \mathrm{s}\) clashes into a rear of a truck of mass \(8000 \mathrm{~kg}\) moving in the same direction with a velocity of \(4 \mathrm{~m} / \mathrm{s}\). After the collision the car bounces with a velocity of \(8 \mathrm{~ms}^{-1}\). The velocity of truck after the impact is \(\mathrm{m} / \mathrm{s}\) (B) 4 (C) 6 (D) 9 (A) 8

The upper half of an inclined plane of inclination \(\theta\) is perfectly smooth while the lower half is rough A body starting from the rest at top come back to rest at the bottom, then the coefficient of friction for the lower half is given by (A) \(\mu=\sin \theta\) (B) \(\mu=\cot \theta\) (C) \(\mu=2 \cos \theta\) (D) \(\mu=2 \tan \theta\)

The motion of a particle of a mass \(m\) is describe by \(\mathrm{y}=\mathrm{ut}+(1 / 2) \mathrm{gt}^{2}\). Find the force acting on the particle. (A) \(\mathrm{F}=\mathrm{ma}\) (B) \(\mathrm{F}=\mathrm{mg} \quad\) (C) \(\mathrm{F}=0\) (D) None of these

A balloon has a mass of \(10 \mathrm{~g}\) in air, The air escapes from the balloon at a uniform rate with a velocity of \(5 \mathrm{~cm} / \mathrm{s}\) and the balloon shrinks completely in \(2.5 \mathrm{sec}\). calculate the average force acting on the balloon. (A) 20 dyne (B) 5 dyne (C) 0 dyne (D) 10 dyne

With what acceleration (a) should a box descend so that a block of mass \(\mathrm{M}\) placed in it exerts a force \((\mathrm{Mg} / 4)\) on the floor of the box? (A) \((4 \mathrm{~g} / 3)\) (B) \((3 \mathrm{~g} / 4)\) (C) \(\mathrm{g} / 4\) (D) \(3 \mathrm{~g}\)

The minimum force required to start pushing a body up a rough (coefficient of) inclined plane is \(\mathrm{F}_{1}\). While the minimum force needed to prevent it from sliding down is \(\mathrm{F}_{2}\). If the inclined plane makes an angle \(\theta\) from the horizontal. such that \(\tan \theta=2 \mu\) than the ratio \(\left(\mathrm{F}_{1} / \mathrm{F}_{2}\right)\) is (A) 4 (B) 1 (C) 2 (D) 3

Assertion and reason are given in following question. Each question have four options. One of them is correct select it. (A) Assertion is true. Reason is true and reason is correct explanation for Assertion. (B) Assertion is true. Reason is true but reason is not the correct explanation of assertion. (C) Assertion is true. Reason is false. (D) Assertion is false. Reason is true. Assertion: A body of mass \(1 \mathrm{~kg}\) is moving with an acceleration of \(1 \mathrm{~ms}^{-1}\) The rate of change of its momentum is \(1 \mathrm{~N}\). Reason: The rate of change of momentum of body \(=\) force applied on the body. (A) a (B) \(\mathrm{b}\) (C) (D) \(\mathrm{d}\)

A cricket ball of mass \(150 \mathrm{~g}\). is moving with a velocity of \(12 \mathrm{~m} / \mathrm{s}\) and is hit by a bat so that the ball is turned back with a velocity of \(20 \mathrm{~m} / \mathrm{s}\). If duration of contact between the ball and the bat is \(0.01 \mathrm{sec}\). The impulse of the force is (A) \(7.4 \mathrm{NS}\) (B) \(4.8 \mathrm{NS}\) (C) \(1.2 \mathrm{NS}\) (D) \(4.7 \mathrm{NS}\)