On a smooth horizontal surface, a ball of mass 1 kg is placed, tied to a nail O on the same horizontal surface with a string of length 50 cm. Another ball of same mass travelling on the horizontal sur

Question

On a smooth horizontal surface, a ball of mass 1 kg is placed, tied to a nail O on the same horizontal surface with a string of length 50 cm. Another ball of same mass travelling on the horizontal surface with a speed of 10 m/s, its velocity making an angle of 4 5 ∘ with string as shown, collides with the first ball. The balls stick to each other after collision :-

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During the collision the string is slack (the blow drives the ball partly toward O), so momentum is conserved and the combined 2 kg moves at 5 m/s at 45° to the string; tension just after collision is zero (A wrong, B correct).

The string stays slack until the balls are again 50 cm from O: straight-line travel $2 \times 50 cos 4 5^{\circ} = 70.7 cm$ at 5 m/s:

$t = \frac{0.707}{5} = 0.141 s$

When the string jerks taut, only the component along the new string direction is lost: $v^{'} = 5 cos 4 5^{\circ} = \frac{5}{2} m/s$ (D correct). Ans. (B,C,D)

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