## A block attached with a spring is placed on a smooth horizontal surface….

Q: A block attached with a spring is placed on a smooth horizontal surface. Now, the block and free end A are project with same speed v0 in opposite directions along the surface as shown in figure . The maximum elongation is (a) $\sqrt{\frac{2 m}{k} v_0}$

(b) $\sqrt{\frac{4 m}{k} v_0}$

(c) $\sqrt{\frac{m}{k} v_0}$

(d) None of these

Ans: (b)
Ans: In the frame of point A ,Initial speed of the block = 2 v0

At the time of maximum elongation block comes to rest in the frame of point A

Now Applying Principle of Conservation of Mechanical Energy

$\displaystyle \frac{1}{2}m (2 v_0)^2 = \frac{1}{2} k x_{max}^2$

$\displaystyle x_{max} = \sqrt{\frac{4 m}{k} v_0}$

## Two blocks each of mass 1 kg are connected by a light spring of spring constant k = 100 N/m….

Q: Two blocks each of mass 1 kg are connected by a light spring of spring constant k = 100 N/m. When spring is in natural length, each block is projected in opposite direction with speed of 10 m/s. The work done by spring on each block upto maximum compression is (a) 100 J

(b) -100 J

(c) 50 J

(d) – 50 J

Ans: (d)

## In the given figure below, a block slides along smooth inclined plane, then moves on rough horizontal surface. The initial height of the block from the ground is H.

Q: In the given figure below, a block slides along smooth inclined plane, then moves on rough horizontal surface. The initial height of the block from the ground is H. (a) When H increases, d decreases

(b) When H decreases, d decreases

(c) H is always equal to d

(d) When mass of the block increases, d increases

Ans: (b)

## The potential energy of a 1 kg particle free to move along the X – axis is given by v(x) = (x^4/4- x^2/2) J. ..

Q: The potential energy of a 1 kg particle free to move along the X – axis is given by $V(x) = \frac{x^4}{4}- \frac{x^2}{2}$ J. The total mechanical energy of the particle is 2 J. Then, the maximum speed (in ms-1) is

(a) 3/√2

(b) √2

(c) 1/√2

(d) 2

Ans: (a)

## A spherical ball of mass 20 kg is stationary on the top of a hill of height 100 m. If rolls down a smooth surface to the horizontal bases at a height of 20 m above the ground….

Q: A spherical ball of mass 20 kg is stationary on the top of a hill of height 100 m. If rolls down a smooth surface to the horizontal bases at a height of 20 m above the ground. The velocity attained by the ball is

(a) 40 m/s

(b) 20 m/s

(c) 10 m/s

(d) 10√30 m/s