First slide

Numericals based on work energy theorem

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

Moderate

A

$\frac{m_{1}}{m_{2}} s_{1}$
B

$\frac{m_{2}}{m_{1}} s_{1}$
C

$\frac{{m_{2}}^{2}}{{m_{1}}^{2}} s_{1}$
D

$\frac{{m_{1}}^{2}}{{m_{2}}^{2}} s_{1}$

Solution

$f r o m c o n s e r v a t i o n o f l i n e a r m o m e t u m t h e y w i l l h a v e s a m e m o m e n t u m b u t i n o p p o s i t e d i r e c t i o n s t h e i r k i n e t i c e n e r g y \frac{p^{2}}{2 m} f r o m w o r k e n e r g y t h e o r e m \frac{p^{2}}{2 m} = μ m g s s i s i n v e r s e l y p r o p o r t i o n o a l t o m^{2}$

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