A small object of uniform density rolls up a curved surface with an initial velocity `v`. It reaches up to a maximum height of `(3v^(2))/(4g)` with respect to the initial position. The object is
(a). Ring
(b). solid sphere
(c). hollow sphere
(d). disc

Options

A. ring
B. solid sphere
C. hollow sphere
D. disc

Answer

D

Explanation

As `v=sqrt((2gh)/(1+(k^(2))/(r^(2))))" Given, h"=(3v^(2))/(4g)`
`v^(2)=(2gh)/(1+(k^(2))/(r^(2)))=(3r^(2)//2)/((1+(k^(2))/(r^(2))))=(v^(2).//2)/((1+(u^(2))/(v^(2))))`
`rArr" "1=(3)/(2(1+(k^(2))/(v^(2))))`
`"or "1+(k^(2))/(r^(2))=(3)/(2)" "rArr" "(k^(2))/(r^(2))=(3)/(2)-1=(1)/(2)`
`k^(2)=(1)/(2)r^(2)" (equation of disc)"`
Hence, the object is disc.