In the shown system, each of the block is at rest. The value of $\mathrm{\theta }$ is:
        
1. ${\tan }^{-1}\left(1\right)$

2. ${\tan }^{-1}\left(\frac{3}{4}\right)$

3. ${\tan }^{-1}\left(\frac{4}{3}\right)$

4. ${\tan }^{-1}\left(\frac{3}{5}\right)$

A block of mass 1 kg lying on the floor is subjected to a horizontal force given by, \(F=2sin\omega t\) newtons. The coefficient of friction between the block and the floor is 0.25. The acceleration of the block will be:
1. positive and uniform
2. positive and non–uniform
3. zero
4. depending on the value of $\mathrm{\omega }$

A body of mass \(5\) kg is suspended by the strings making angles $60°$and $30°$with the horizontal.

Then:
a. ${\mathrm{T}}_1=25$ $\mathrm{N}$                    
b. ${\mathrm{T}}_2=25$ $\mathrm{N}$
c. ${\mathrm{T}}_1=25\sqrt{3}$ $\mathrm{N}$               
d. ${\mathrm{T}}_2=25\sqrt{3}$ $\mathrm{N}$
Choose the correct option:

A 5 m long uniformly thick string rests on a horizontal frictionless surface. It is pulled by a horizontal force of 5 N from one end. The tension in the string at 1 m from the end where the force is applied is:

The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1. ${\tan }^{-1}(0.25)$
2. ${\tan }^{-1}(0.55)$
3. ${\tan }^{-1}(0.45)$
4. ${\tan }^{-1}(0.75)$

A man of mass m stands on a crate of mass \(\text {M}\). He pulls on a light rope, passing over a smooth light pulley. The other end of the rope is attached to the crate. For the system to be in equilibrium, the force exerted by the man on the rope will be:
    

At a wall, N bullets, each of mass m, are fired with a velocity v at the rate of n bullets/sec upon the wall. The bullets are stopped by the wall. The reaction offered by the wall to the bullets is:

1. $\frac{\mathrm{Nmv}}{\mathrm{n}}$

2. nNmv

3. $\mathrm{n}\frac{\mathrm{Nv}}{\mathrm{m}}$

4. nmv

A block of mass \(10~\text{kg}\) is in contact with the inner wall of a hollow cylindrical drum of radius \(1~\text{m}\). 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: \(\left(g= 10~\text{m/s}^2\right )\)
1. \(10~\pi~\text{rad/s}\)
2. \(\sqrt{10}~\pi~\text{rad/s}\)
3. \(\frac{10}{2\pi}~\text{rad/s}\)
4. \(10~\text{rad/s}\)

A tube of length \(\text L\) is filled completely with an incompressible liquid of mass \(\text M\) 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:

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 \(\vec F\) where:
1. \(|{\vec F}| = mg+\mu mg\)
2. \(|\vec F| =\mu mg\)
3. \(|\vec F| \le mg\sqrt{1+\mu^2}\)
4. \(|\vec F| = mg\)