NLM

In the figure masses $m_{1}$ , $m_{2}$ and M are 20 kg, 5 kg and 50 kg respectively. The co-efficient of friction between M and ground is zero. The co-efficient of friction between $m_{1}$ and M and that between $m_{2}$ and ground is 0.3. The pulleys and the string are massless. The string is perfectly horizontal between $P_{1}$ and $m_{1}$ and also between $P_{2}$ and $m_{2}$ . The string is perfectly vertical between $P_{1}$ and $P_{2}$ . An external horizontal force F is applied to the mass M. Take $g = 10 \, m/s^{2}$ . (I) Draw a free-body diagram for mass M, clearly showing all the forces. (II) Let the magnitude of the force of friction between $m_{1}$ and M be $f_{1}$ and that between $m_{2}$ and ground be $f_{2}$ . For a particular F it is found that $f_{1} = 2f_{2}$ . Find $f_{1}$ and $f_{2}$ . Write down equations of motion of all the masses. Find F, tension in the string and accelerations of the masses.

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $\theta$ as shown in figure. The coefficient of kinetic friction is $\mu_{K}$ . Then, the block's acceleration 'a' is given by: (g is acceleration due to gravity)

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given

A block B is tied to one end of a uniform rope R as shown. The mass of block is 2 kg and that of rope is 1 kg. A force F = 15 N is applied at angle $37^{\circ}$ with vertical. The tension at the mid-point of rope is

Same spring is attached with 2 kg, 3 kg and 1 kg blocks in three different cases as shown. If $x_{1}$ , $x_{2}$ and $x_{3}$ be the extensions in the spring in these three cases, when acceleration of both the blocks have same magnitude, then

Three boxes are placed in a lift. When acceleration of the lift is $4 \, m/s^{2}$ , the net force on the 8 kg box is closest to

Reading shown in two spring balances $S_{1}$ and $S_{2}$ is 90 kg and 30 kg respectively when lift is accelerating upwards with acceleration $10 \, m/s^{2}$ . The mass is stationary with respect to lift. Then the mass of the block will be :

On one rainy day, a sports car starts moving with a constant acceleration of $7.5 \, m/s^2$ . If a toy monkey is suspended from the ceiling of the car by a string, then at what angle the string is inclined with the vertical?

A block is placed on a rough horizontal surface. The coefficient of friction between block and surface is 0.5. A time dependent force $F = -t^2 + 6t$ is acting on the block for time $t = 0$ to $t = 6$ sec as shown in figure. Then which statement is incorrect?

A lift is going upward when suddenly cable supporting the lift breaks. From a reference frame attached to the lift, pseudo force acting on an object will have direction (After the cable broke) :-

In the figure as shown if 2kg block is moving at an acceleration of $2m/s^{2}$ towards right, find the elongation in spring and acceleration of 4kg block at this instant. Take $g = 10\ m/s^{2}$ .

A small electrically charged sphere is suspended vertically from a thread. An oppositely charged rod is brought close to the sphere such that the sphere is in equilibrium displaced from the vertical by an angle of $30^{\circ}$ . Which one of the following best represents the free body diagram for the sphere?

Two monkeys of masses 10 kg and 8 kg are moving along a vertical light rope, the former climbing up with an acceleration of $2 \, m/s^{2}$ , while the latter coming down with a uniform velocity of 2 m/s. Find tension in the rope at the fixed support.

In the arrangement shown in fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed.

As shown in figure a wedge of mass 2kg is resting on frictionless floor. A block of mass 1kg is kept on the wedge and the wedge is given an acceleration of $5 \, m/sec^{2}$ towards right. Then:

A block of mass 2 kg is kept on a rough horizontal floor and pulled with a force F. If the coefficient of friction is 0.5, then the minimum force required to move the block is :-

A force $\vec{F} = \hat{i} + 4\hat{j}$ acts on block as shown. The force of friction acting on the block is :

Block B of mass 100 kg rests on a rough surface of friction coefficient $\mu = 1/3$ . A rope is tied to block B as shown in figure. The maximum acceleration with which boy A of mass 25 kg can climbs on rope without making block move is :

The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 m away from the open end, m = 0.15 kg and $g = 10 \, m/s^{2}$ . The truck starts from rest with an acceleration of $2m/s^{2}$ on a straight road. The distance moved by the truck when box falls down from the truck is:

A block is pushed with some velocity up a rough inclined plane. It stops after ascending few meters and then reverses its direction and returns back to point from where it started. If angle of inclination is $37^{\circ}$ and the time to climb up is half of the time to return back then coefficient of friction is

The system is pushed by a force F as shown in figure. All surfaces are smooth except between B and C. Friction coefficient between B and C is $\mu$ . Minimum value of F to prevent block B from downward slipping is :-

The coefficient of static and kinetic friction between the two blocks and also between the lower block and the ground are $\mu_{S} = 0.6$ and $\mu_{K} = 0.4$ . Find the value of tension T applied on the lower block at which the upper block begins to slip relative to lower block.

Two blocks of masses 2.0 kg and 3.0 kg are connected by light inextensible string. The string passes over an ideal pulley pivoted to a fixed axle on a smooth incline plane as shown in the figure. When the blocks are released, find magnitude of their accelerations $(m/s^{2})$ .

A 1kg block B rests as shown on a bracket A of same mass. Constant forces $F_{1} = 20N$ and $F_{2} = 8N$ start to act at time t = 0 when the distance of block B from pulley is 50cm. Time (s) when block B reaches the pulley is $\frac{1}{n}$ , find the value of n.

In the system shown, the blocks A, B and C are of weight 4W, W and W respectively. The system set free. The tension in the string connecting the blocks B and C is (W = 30N)