Question 289: Work, Energy and Power & Circular Motion

Question

A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is __________ m.
(Assume there is no friction between the block and the hemisphere)

Accepted Answer

$$mg\cos 	heta  = {{m{v^2}} \over R}$$ .... (1)
$$\cos 	heta  = {h \over R}$$
Energy conservation
$$mg\{ R - h\}  = {1 \over 2}m{v^2}$$ ..... (2)
from (1) & (2)
$$\Rightarrow$$ $$mg\left\{ {{h \over R}} ight\} = {{2mg\{ R - h\} } \over R}$$
$$h = {{2R} \over 3}$$ = 2m

Work, Energy and Power & Circular Motion

A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is __________ m. (Assume there is no friction between the block and the hemisphere)

Integer / Numeric Answer Type