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A block of mass 2kg rests on a rough inclined plane making an of ${30}^{°}$ with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is
1. 9.8 N
2. $0.7\times 9.8\times \sqrt{3}$N
3. $9.8\times \sqrt{3}$N
4. 0.7$\times$9.8 N

The strings between blocks of mass m and 2m is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut find the magnitudes of accelerations of mass 2m and m (immediately after cutting)

1. g, g
2. g, $\frac{\mathrm{g}}{2}$
3. $\frac{\mathrm{g}}{2}, g$
4. $\frac{\mathrm{g}}{2}, \frac{g}{2}$

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

1. always radially outwards
2. always radially inwards
3. radially outwards initially and radially inwards later
4. radially inwards initially and radially outwards later

Three forces start acting simultaneously on a particle moving with velocity, $\overrightarrow{\mathrm{v}}$. these forces are represented in magnitude and direction by the three sides of a triangle ABC. The particle will now move with velocity.

1. less than $\overrightarrow{\mathrm{v}}$
2. greater than $\overrightarrow{\mathrm{v}}$
3. $\left|\mathrm{v}\right|$ in the direction of the largest force BC
4. $\overrightarrow{\mathrm{v}}$, remaining unchanged

The upper half of an inclined plane with inclination $\mathrm{\varphi }$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
1. 2 cos $\mathrm{\varphi }$
2. 2 sin $\mathrm{\varphi }$
3. tan $\mathrm{\varphi }$
4. 2 tan $\mathrm{\varphi }$

Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is:

1. 120 N
2. 150 N
3.. 100 N
4. 80 N

Two particles of masses ${\mathrm{m}}_1 \mathrm{and} {\mathrm{m}}_2$ in projectile motion have velocities $\overrightarrow{{\mathrm{v}}_1} and \overrightarrow{v_2}$ respectively at time t = 0. the collide at time ${\mathrm{t}}_0$. Their velocities become $\overrightarrow{{\mathrm{v}}_1}\text{'} and \overrightarrow{{\mathrm{v}}_2}\text{'}$ at the time $2{\mathrm{t}}_0$ while still moving in air. The value of $\left|\left({\mathrm{m}}_1\overrightarrow{{\mathrm{v}}_1}\text{'}+{\mathrm{m}}_2\overrightarrow{{\mathrm{v}}_2}\text{'}\right)\right|-\left|\left({\mathrm{m}}_1\overrightarrow{{\mathrm{v}}_1}+{\mathrm{m}}_2\overrightarrow{{\mathrm{v}}_2}\right)\right|$ is 
1. zero
2. $\left({\mathrm{m}}_1+{\mathrm{m}}_2\right)g{t}_0$
3. $\frac{1}{2}(m_1+m_2)g{t}_0$
4. $2({\mathrm{m}}_1+{\mathrm{m}}_2){\mathrm{gt}}_0$

A ball of mass 0.2 kg rests on a vertical post of height 5m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. the ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is 

1. 250 m/s
2. $250\sqrt{2 } \mathrm{m}/\mathrm{s}$
3. 400 m/s
4. 500 m/s

A shell is fired from a cannon with the velocity v (m/sec.) at an angle $\mathrm{\theta }$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retracts its path to the cannon and the speed (in m/sec) of the other piece immediately after the explosion is 
1. 3v cos $\mathrm{\theta }$
2. 2v cos $\mathrm{\theta }$
3. $\frac{3}{2}v \cos \mathrm{\theta }$
4. $\sqrt{\frac{3}{2}}v \cos \theta$

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of$2 {\mathrm{ms}}^{-1}$. Which of the following statement (s) is (are) correct for the system of these two masses?
1. Total momentum of the system is $3 \mathrm{kg} {\mathrm{ms}}^{-1}$
2. Momentum of 5 kg mass after collision is $4 \mathrm{kg} {\mathrm{ms}}^{-1}$
3. Kinetic energy of the centre of the mass is 0.75 J.
4. Total kinetic energy of the system is 4 J.

Statement - 1 : In an elastic collision between two bodies, ,the relative speed of the bodies after collision is equal to the relative speed before the collision.
Statement - 2 : In an elastic collision, the linear momentum of the system is conserved.
1. Statement - 1 is true, Statement - 2 is true; statement - 2 is correct explanation for statement -1.
2. Statement - 1 is true, statement - 2 is true; statement - 2 is not correct explanation for statement - 1.
3. Statement - 1 is true, statement - 2 is false.
4. Statement - 1 is false, statement - 2 is true.

Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement - 2 : Principle of conservation of momentum holds true for all kinds of collisions.
1. Statement - 1 is true, statement - 2 is true; statement - 2 is the correct explanation of statement -1 
2. Statement - 1 is true, statement - 2 is true; statement -2 is not the correct explanation of statement - 1
3. Statement - 1 is false, statement - 2 is true.
4. Statement - 1 is true, statement - 2 is false.

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in
1. 
2. 
3. 
4. 

A block of mass 0.1 kg is held against a wall aplying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is:
1. 2.5 N
2. 0.98 N
3. 4.9 N
4. 0.49 N

An insect crawl up a hemispherical surface very slowly (see fig.). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle $\mathrm{\alpha }$with the vertical, the maximum possible value of $\mathrm{\alpha }$ is given by

1. $\cot \mathrm{\alpha }=3$
2. $\tan \mathrm{\alpha }=3$
3. $\sec \mathrm{\alpha }=3$
4. $\cos ec \mathrm{\alpha }=3$