A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. In the frame of the truck, the pendulum will tilt:

1. to the left and angle of inclination of the pendulum with the vertical is ${\sin }^{-1}\left(\frac{a}{g}\right)$

2. to the left and angle of inclination of the pendulum with the vertical is ${\cos }^{-1}\left(\frac{a}{g}\right)$

3. to the left and angle of inclination of the pendulum with the vertical is ${\tan }^{-1}\left(\frac{a}{g}\right)$

4. to the left and angle of inclination of the pendulum with the vertical is ${\tan }^{-1}\left(\frac{g}{a}\right)$

A body of mass m is kept on a rough horizontal surface (coefficient of friction= $\mu$). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\overrightarrow{F}$, where:

1. $\left|\overrightarrow{F}\right|=mg+\mu mg$

2. $\left|\overrightarrow{F}\right|=\mu mg$

3. $\left|\overrightarrow{F}\right|\le mg\sqrt{1+{\mu }^2}$

4. $\left|\overrightarrow{F}\right|=mg$

A particle moving with velocity $\overrightarrow{v}$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will:

1. change according to the smallest force $\overrightarrow{QR}$.

2. increase.

3. decrease.

4. remain constant.

A block of mass 10 kg is in contact with the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder, which is vertical and rotating about its axis, will be:
(g=10 m/s²)

1. $10 \mathrm{\pi } \mathrm{rad}/\mathrm{s}$

2. $\sqrt{10} \mathrm{\pi } \mathrm{rad}/\mathrm{s}$

3. $\frac{10}{2\mathrm{\pi }} \mathrm{rad}/\mathrm{s}$

4. $10 \mathrm{rad}/\mathrm{s}$

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is:

1. $\frac{ML{\omega }^2}{2}$

2. $\frac{M{L}^2\omega }{2}$

3. $ML{\omega }^2$

4. $\frac{M{L}^2{\omega }^2}{2}$

A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of ${30}^{\mathrm{o}}$ 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 s, the average force acting on the wall is:

1. 48 N

2. 24 N

3. 12 N

4. 96 N

A block B is pushed momentarily along a horizontal surface with an initial velocity 'v'. If μ is the coefficient of sliding friction between B and the surface, the block B will come to rest after a time: 
 

1. $\frac{v}{g\mu }$

2. $\frac{g\mu }{v}$

3. $\frac{g}{v}$

4. $\frac{v}{g}$

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be:

1.  Mv Newton

2.  2Mv Newton

3.  $\frac{\mathrm{Mv}}{2}$ Newton

4.  zero

A body, under the action of a force $\overrightarrow{\mathrm{F}}=6\hat{i}-8\hat{j}+10\hat{k}$, acquires an acceleration of 1 ms^-2. The mass of this body must be:

1. 2 √10 kg

2. 10 kg

3. 20 kg

4. 10 √2 kg