Question

A ball of mass m $=$ 200 gm is suspended from a point A by an inextensible string of length L. Ball is drawn to a side and held at same level as A but at a distance $\frac{\sqrt{3}}{2}$L from A as shown. Now the ball is released. Then: (assume string applies only that much jerk which is required so that velocity along string becomes zero).

• A. speed of ball just before experiencing jerk is $\sqrt{gL}$
• B. speed of ball just after experiencing jerk is $\frac{\sqrt{3gL}}{2}$
• C. Impulse applied by string $\frac{\sqrt{gL}}{10}$
• D. ball will experience jerk after reaching to point B.

Answer 1

Answer: (A), (B), (C)

The correct options are
A speed of ball just before experiencing jerk is $\sqrt{gL}$
B speed of ball just after experiencing jerk is $\frac{\sqrt{3gL}}{2}$
C Impulse applied by string $\frac{\sqrt{gL}}{10}$

By conservation of energy

$\frac{1}{2}m{v}^2=mg\frac{L}{2}\Rightarrow v=\sqrt{gL}$

After jerk $vsin$$\theta$ becomes zero
Impulse applied by string $=mvsin\theta$

$=0.2\sqrt{gL}\frac{1}{2}=\frac{\sqrt{gL}}{10}$

velocity of ball after jerk

$vcos$ $\theta =\sqrt{gL}\frac{\sqrt{3}}{2}$

$=\frac{\sqrt{3gL}}{2}.$