A stone of mass 2 kg is projected upward with kinetic energy of 98 J. The height at which the kinetic energy of the stone becomes half its original value, is given by 

Options

A. 5 m
B. 2.5 m
C. 1.5 m
D. 0.5 m

Answer

B

Explanation

At the time of projection kinetic energy of the stone,
`K = 1/2 m u^2`
where m is the mass of the stone and u is the velocity of the projection.
or `mu^2 = (2K)/(m) = (2 xx 98)/(2) = 98`
Let h be the maximum height attained by the stone.
`:. h = (u^2)/(2g) or h = (98)/(2 xx 9.8) = 5 m " " .....(i)`
Also, `K = 1/2 m (2gh) " " `(Using (i))
Let h. be the height at which the kinetic energy of hte stone becomes half.
`:. K. = 1/2 m (2 gh.)`
`:. (K.)/K = (h.)/h ` But `K. = K/2 :. K/(2K) = (h.)/(h)`
or `h. = h/2 = 5/2 m = 2.5 m`.