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A thin spherical shell of radius R lying...

A thin spherical shell of radius `R` lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?

Text Solution

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Let `vz` be the velocity attained by its centre of mass and `omega` be the angular velocity about the centre of mass by the impact of the cue.

Suppose `J` is the impulse provided `y` the cube
`J=m(v-0)`…..i
and `J.h=l(omega-0)`.............ii
From eqn i and ii `Mvxxh=Iomega`
For pure rolling `omega=v/R`
`:. mvxxh=2/3mR^(2)xxv/R`
`impliesh=(2R)/3`
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