A small body of mass m slides without friction from the top of a hemispherical cup of radius r as shown in the following figure. If it leaves the surface of the cup at a vertical distance h below the highest point, then-
A
h=r
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B
h=r3
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C
h=r2
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D
h=2r3
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Solution
The correct option is Bh=r3
mgcosθ−N=fc
when the mass m detaches from hemispere, N=0 mgcosθ=fc=mv2r v2=grcosθ...(i)
from conservation of mechanical energy mgr+0=mg(r−h)+12mv2 mgr=m(g(r−h)+12grcosθ) gr=g((r−h)+12r×r−hr) r=(r−h)+12(r−h) r=3(r−h)2 h=r3