Question

Two balls of masses $m _ { 1 }$ and $m _ { 2 }$ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass $m _ { 1 }$ travels a distance $S _ { 1 }$ and stops. If the coefficients of friction between the balls and ground are same, the mass $m _ { 2 }$ stops after travelling the distance

• A. $s _ { 2 } = \frac { m _ { 1 } } { m _ { 2 } } s _ { 1 }$
• B. $s _ { 2 } = \frac { m _ { 2 } } { m _ { 1 } } s _ { 1 }$
• C. $s _ { 2 } = \frac { m _ { 1 } ^ { 2 } } { m _ { 2 } ^ { 2 } } s _ { 1 }$
• D. $s _ { 2 } = \frac { m _ { 2 } ^ { 2 } } { m _ { 1 } ^ { 2 } } s _ { 1 }$

Answer 1

Answer: (C)

$s _ { 2 } = \frac { m _ { 1 } ^ { 2 } } { m _ { 2 } ^ { 2 } } s _ { 1 }$

Answer 2

We know that in the given condition $s \propto \frac { 1 } { m ^ { 2 } }$

$\therefore$ $\frac { s _ { 2 } } { s _ { 1 } } = \left( \frac { m _ { 1 } } { m _ { 2 } } \right) ^ { 2 }$ ⇒ $s _ { 2 } = \left( \frac { m _ { 1 } } { m _ { 2 } } \right) ^ { 2 } \times s _ { 1 }$