The kinetic energy of a body is increased by 21%. The percentage increase in the magnitude of linear momentum of the body will be:

1.  10%

2.  20%

3.  Zero

4.  11.5%

A rigid body of mass \(m\) is moving in a circle of radius \(r\) with constant speed \(v.\) The force on the body is \(\dfrac{mv^2}{r}\) and is always directed towards the centre. The work done by this force in moving the body over half the circumference of the circle will be:
1. \(\dfrac{mv^{2}}{rπ}\) 
2. \(mr^{2} \pi\)
3. zero
4. \(2 mv^{2} \pi\)$\mathrm{}$

A particle of mass \(10\) kg moves with a velocity of \(10\sqrt{x}\) in SI units, where \(x\) is displacement. The work done by the net force during the displacement of the particle from \(x=4~\text{m}\) to \(x= 9~\text{m}\) is:
1. \(1250~\text{J}\)
2. \(1000~\text{J}\)
3. \(3500~\text{J}\)
4. \(2500~\text{J}\)

The potential energy of a particle of mass m varies as the magnitude of the $U=a{x}^2+by.$ The magnitude of the acceleration of the particle at (0, 3) is: (symbols have their usual meaning)

1.  $\sqrt{\frac{\mathrm{b}}{\mathrm{m}}}$

2.  $\sqrt{\frac{3\mathrm{b}}{\mathrm{m}}}$

3.  $\frac{\mathrm{b}}{\mathrm{m}}$

4.  Zero

A block is released from rest from a height of \(h = 5 ~\text m.\) After traveling through the smooth curved surface, it moves on the rough horizontal surface through a length \(l = 8 ~\text m\) and climbs onto the other smooth curved surface at a height \(h'.\) If $\mathrm{}$\(μ = 0.5,\) then the height \( h'\) is:

If a stone is projected vertically upward from the ground at a speed of 10 m/s, then it's: (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

1.  Potential energy will be maximum after 0.5 s

2.  Kinetic energy will be maximum again after 1 s

3.  Kinetic energy = potential energy at a height of 2.5 m from the ground

4.  Potential energy will be minimum after 1 s

When a spring is subjected to 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

If two springs, A and B $(K_A$ $=$ $2$ $K_B),$ are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:
1.  1 : 2
2.  2 : 1
3.  1 : 1
4.  1 : 4