A point mass \(m\) is moved in a vertical circle of radius \(r\) with the help of a string. The velocity of the mass is \(\sqrt{7 g r} \) at the lowest point. The tension in the string at the lowest point will be: 
1. \(6mg\)
2. \(7mg\)
3. \(8mg\)
4. \(mg\)

A rocket with a lift-off mass of \(20,000\) \(\mathrm{kg}\) is blasted upwards with an initial acceleration of \(5~\mathrm{ms}^{-2}\). Then initial thrust (force) of the blast is:
(Take \(g=10\) \(\mathrm{ms}^{-2}\))
1. \(7 \times 10^5 \mathrm{~N} \)
2. \(0 \)
3. \(2 \times 10^5 \mathrm{~N} \)
4. \(3 \times 10^5 \mathrm{~N}\)

A body of mass \(10 ~\text{Kg}\) is acted upon by two perpendicular forces, \(6 ~\text{N}\) and \(8 ~\text{N}.\) The resultant acceleration of the body is:

If \(\mu\) between block \(A\) and inclined plane is \(0.5\) and that between block \(B\) and the inclined plane is \(0.8,\) then the normal reaction between blocks \(A\) and \(B\) will be:
                       
1. \(180~\text N\) 
2. \(216~\text N\) 
3. \(0\)
4. none of these

What will be the reading of the spring balance in the given setup?  (take \(g=10~\text{m/s}^2\) )
                

1. \(60~\text N\) 
2. \(40~\text N\)
3.  \(50~\text N\) 
4. \(80~\text N\) 

A body of mass \(m\) is moving on a concave bridge \(ABC\) of the radius of curvature \(R\) at a speed \(v.\) The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:

1. \(mg-\frac{mv^{2}}{R}\)
2. \(mg+\frac{mv^{2}}{R}\)
3. \(mg\)
4. \(\frac{mv^{2}}{R}\)

A block of mass \(3\) kg is placed on a rough surface \((\mu=0.2)\) and a variable force acts on it. Variation of acceleration of block with time is correctly shown by the graph:

1.		2.
3.		4.

The kinetic energy \(K\) of a particle moving in a circular path varies with the distance covered \(S\) as \(K = aS^2\) where \(a\) is constant. The angle between the tangential force and the net force acting on the particle is: (\(R\) is the radius of the circular path)
1. \(\tan^{-1}\left(\frac{S}{R}\right)\)
2. \(\tan^{-1}\left(\frac{R}{S}\right)\)
3. \(\tan^{-1}\left(\frac{a}{R}\right)\)
4. \(\tan^{-1}\left(\frac{R}{a}\right)\)

Two blocks of masses \(2\) kg and \(3\) kg placed on a horizontal surface are connected by a massless string. If \(3~\text{kg}\) is pulled by \(10\) N as shown in the figure, then the force of friction acting on the \(2~\text{kg}\) block will be:
(Take \(g=10~\text{m/s}^2\))$\mathrm{}$

On the application of an impulsive force, a sphere of mass \(500\) grams starts moving with an acceleration of \(10\) m/s². The force acts on it for \(0.5\) s. The gain in the momentum of the sphere will be:
1. \(2.5\) kg-m/s
2. \(5\) kg-m/s
3. \(0.05\) kg-m/s
4. \(25\) kg-m/s