Chapter 3

Four forces act on a point object. The object will be in equilibrium if (A) all of them are in the same plane (B) they are opposite to each other in pair (C) the sum of \(x, y\) and \(z\) components of all the force is zero separately (D) they are from a closed figure of four sides

A block of mass \(10 \mathrm{~kg}\) is placed on a rough inclined plane of inclination \(37^{\circ}\left(\tan 37^{\circ}=3 / 4\right)\). The co-efficient of friction between block and surface is \(0.4\). A horizontal force \(F=50 \mathrm{~N}\) is applied on the block, then \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) Acceleration of block is zero. (B) Acceleration of block is \(2.4 \mathrm{~m} / \mathrm{s}^{2}\) along the inclined plane. (C) Frictional force between block and surface is \(44 \mathrm{~N}\). (D) Frictional force between block and surface is \(20 \mathrm{~N}\).

A block \(P\) of mass \(4 \mathrm{~kg}\) is placed on horizontal rough surface with co-efficient of friction \(\mu=0.6\). And two blocks \(R\) and \(Q\) of masses \(2 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) connected with the help of massless strings \(A\) and \(B\), respectively, passing over frictionless pulleys as shown, then \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) Acceleration of block \(P\) is zero. (B) Tension in string \(A\) is \(20 \mathrm{~N}\). (C) Tension in string \(B\) is \(40 \mathrm{~N}\). (D) Contact force on block \(P\) is \(20 \sqrt{5} \mathrm{~N}\).

Reading of the spring scale in figure (B) (A) \(90 \mathrm{~N}\) (B) \(62.5 \mathrm{~N}\) (C) \(55 \mathrm{~N}\) (D) \(75 \mathrm{~N}\)

A block of mass \(5 \mathrm{~kg}\) is kept on a rough horizontal floor. It's given velocity is \(33 \mathrm{~m} / \mathrm{s}\) towards right. A force of \(20 \sqrt{2} \mathrm{~N}\) continuously acts on the block as shown. If the co- efficient of friction between block and floor is \(0.5\), find the velocity of the block after 5 seconds \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\).

Two blocks of masses \(5 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are placed on a smooth horizontal surface. A horizontal force \(F=16 \mathrm{~N}\) is applied on \(5 \mathrm{~kg}\) as shown. Find normal force between the blocks.

A small block of mass \(m\) is placed in a groove carved inside a disc. The disc is placed on smooth horizontal surface and pulled with an acceleration of magnitude \(25 \mathrm{~m} / \mathrm{s}^{2}\) as shown. Find half of the acceleration of block with respect to the disc in \(\mathrm{m} / \mathrm{s}^{2}\) ? (Given \(\sin \theta=\frac{3}{5}, \cos \theta=\frac{4}{5}, g=10 \mathrm{~m} / \mathrm{s}^{2} \quad\) and co-efficient of friction between groove and the block is \(\mu=\frac{2}{5}\) )

A light string passing over a smooth light pulley connects two blocks of masses \(m_{1}\) and \(m_{2}\) (vertically). If the acceleration of the system is \(g / 8\), then the ratio of the masses is (A) \(8: 1\) (B) \(9: 7\) (C) \(4: 3\) (D) \(5: 3\)

Three identical blocks of masses \(m=2 \mathrm{~kg}\) each are drawn by a force \(F=10.2 \mathrm{~N}\) with an acceleration of \(0.6 \mathrm{~m} / \mathrm{s}^{2}\) on a surface, then what is the tension (in N) in the string between \(B\) and \(C\), if there is no friction between the surface and the blocks \(A\) and \(B\) (A) \(9.2\) (B) \(3.4\) (C) 4 (D) \(9.8\)

One end of massless rope, which passes over a massless and frictionless pulley \(P\) is tied to a hook \(C\) while the other end is free. Maximum tension that the rope can bear is \(840 \mathrm{~N}\). With what value of maximum safe acceleration (in \(\mathrm{ms}^{-2}\) ) can a man of \(60 \mathrm{~kg}\) climb on the rope? (A) 16 (B) 6 (C) 4 (D) 8

A lift is moving down with an acceleration \(a\). A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are, respectively, (A) \(g, g\) (B) \(g-a, g,-a\) (C) \(g-a, g\) (D) \(a, g\)

A horizontal force of \(10 \mathrm{~N}\) is necessary to just hold a block stationary against a wall. The co-efficient of friction between the block and wall is \(0.2\). The weight of the block is (A) \(20 \mathrm{~N}\) (B) \(50 \mathrm{~N}\) (C) \(100 \mathrm{~N}\) (D) \(2 \mathrm{~N}\)

A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(m\). If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block is (A) \(\frac{P m}{M+m}\) (B) \(\frac{P m}{M-m}\) (C) \(P\) (D) \(\frac{P M}{M+m}\)

A light spring balance hangs from the hook of the other light spring balance and a block of mass \(M \mathrm{~kg}\) hangs from the former one. Then the true statement about the scale reading is (A) Both the scales read \(M \mathrm{~kg}\) each (B) The scale of the lower one reads \(M \mathrm{~kg}\) and of the upper one zero (C) The reading of the two scales can be anything but the sum of the readings will be \(M \mathrm{~kg}\) (D) Both the scales read \(M / 2 \mathrm{~kg}\)

A block rests on a rough inclined plane making an angle of \(30^{\circ}\) with the horizontal. The co-efficient of static friction between the block and the plane is \(0.8\). If the frictional force on the block is \(10 \mathrm{~N}\), the mass of the block (in \(\mathrm{kg}\) ) is (Taking \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) ) (A) \(2.0\) (B) \(4.0\) (C) \(1.6\) (D) \(2.5\)

Two masses \(m_{1}=5 \mathrm{~kg}\) and \(m_{2}=4.8 \mathrm{~kg}\) tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when they are free to move? \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right) \quad\) (A) \(0.2 \mathrm{~m} / \mathrm{s}^{2}\) (B) \(9.8 \mathrm{~m} / \mathrm{s}^{2}\) (C) \(5 \mathrm{~m} / \mathrm{s}^{2}\) (D) \(4.8 \mathrm{~m} / \mathrm{s}^{2}\)

A block is kept on a frictionless inclined surface with angle of inclination \(\alpha\). The incline is given an acceleration a to keep the block stationary with respect to the incline. Then a is equal to (A) \(g / \tan \alpha\) (B) \(g \operatorname{cosec} \alpha\) (C) \(g\) (D) \(g \tan \alpha\)

A block of mass \(m\) is connected to another block of mass \(M\) by a spring (massless) of spring constant \(k\). The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force \(F\) starts acting on the block of mass \(M\) to pull it. Find the force on the block of mass \(m .\) (A) \(\frac{m F}{M}\) (B) \(\frac{(M+m) F}{m}\) (C) \(\frac{m F}{(m+M)}\) (D) \(\frac{M F}{(m+M)}\)

A block of mass \(m\) is placed on a surface with a vertical cross-section given by \(y=\frac{x^{3}}{6} .\) If the co-efficient of friction is \(0.5\), the maximum height above the ground at which the block can be placed without slipping is: (A) \(\frac{1}{6} m\) (B) \(\frac{2}{3} m\) (C) \(\frac{1}{3} m\) (D) \(\frac{1}{2} m\)