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  • A thin spherical shell lies on a rough horizontal  plane, this shell has mass 1 Kg and radius 1m. A particle of mass 100 grams is travelling at a speed of  10 m/s hits the sphere at

A thin spherical shell lies on a rough horizontal  plane, this shell has mass 1 Kg and radius 1m. A particle of mass 100 grams is travelling at a speed of  10 m/s hits the sphere at a height of 0.5 m from the bottom and immediately comes to rest. Then the angular velocity of the shell just after the collision will be.


 

Option: 1

\frac{1}{4}\, \mathrm{rad} / \mathrm{s}


Option: 2

\frac{1}{2} \,\mathrm{rad} / \mathrm{s}


Option: 3

\frac{3}{4}\, \mathrm{rad} / \mathrm{s}


Option: 4

1 \,\mathrm{rad} / \mathrm{s}


Answers (1)

best_answer

Using conservation of momentum

0.1 \times 10 =1 \times U_{\mathrm{c.m}} \\

U_{c . m} =1 \mathrm{~m} / \mathrm{s}

Taking angular momentum along the direction of motion of the particle.

L_i =0 \\

L_f =\frac{2}{3} M R^2 \omega-M(R-h) U_{c \cdot m} \\

L_f =0 \\

\frac{2}{3} M R^2 \omega =M(R-h) U_{c \cdot m} \\

\frac{2}{3} \times(1)^2 \times \omega =(1-0.5) U_{c \cdot m} \\

\frac{2}{3} \omega =\frac{U_{c \cdot m}}{2} \\

\omega =\frac{3}{4} \times 1=\frac{3}{4} \mathrm{rad} / \mathrm{s}

Posted by

jitender.kumar

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