Q.

A hemispherical shell of mass M and radius R is hinged at point O and palced on a horizontal surface. A ball of mass M moving with a velocity u inclined at an angle α=tan112 strikes the shell at point A (as shown in the figure) and stops. What is the minimum speed u if the given shell is to reach the horizontal surface OP?

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a

Zero

b

2gR3

c

gR5

d

it cannot come on the surface for any value of u

answer is D.

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Detailed Solution

There is neither torque nor angular momentam of the colliding particle about the O. (because line of action of its linear momentum  passes through O) So u = 0.

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A hemispherical shell of mass M and radius R is hinged at point O and palced on a horizontal surface. A ball of mass M moving with a velocity u inclined at an angle α=tan−112 strikes the shell at point A (as shown in the figure) and stops. What is the minimum speed u if the given shell is to reach the horizontal surface OP?