A solid sphere of mass M of radius R is moving with speed ms–1 in free space. Due to application of external impulsive force, it breaks into eight spheres of same radius in such a way that the total mechanical energy before breaking and after breaking of sphere remains same. Find the speed of each sphere V in m/s when separation between them is very large (assume at that instant speed of each sphere is same). Fill the value of in OMR.

Engineering

Physics

Gravitational Force and Field

Question

A solid sphere of mass M of radius R is moving with speed $\sqrt{\frac{GM}{R}} = 100 \sqrt{10}$ ms^–1 in free space. Due to application of external impulsive force, it breaks into eight spheres of same radius in such a way that the total mechanical energy before breaking and after breaking of sphere remains same. Find the speed of each sphere V in m/s when separation between them is very large (assume at that instant speed of each sphere is same). Fill the value of $\frac{V}{25}$ in OMR.

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Using conservation of energy

$- \frac{3 {GM}^{2}}{5 R} + \frac{1}{2} {MV}_{0}^{2}$

$\Rightarrow - \frac{3 G {(M / 8)}^{2}}{5 (R / 2)} \times 8 + \frac{1}{2} \frac{M}{8} \times 8 V^{2}$
$\Rightarrow - \frac{3 {GM}^{2}}{5 R} + \frac{1}{2} {MV}_{0}^{2} = - \frac{3 {GM}^{2}}{20 R} + \frac{1}{2} {MV}^{2}$

$\Rightarrow - \frac{3 GM}{5 R} + \frac{GM}{2 R} + \frac{3 GM}{20 R} = \frac{V^{2}}{2}$

$\Rightarrow \frac{GM}{20 R} = \frac{V^{2}}{R} \Rightarrow V = \sqrt{\frac{GM}{10 R}}$

= 100 M/S