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A small object of uniform density rolls ...

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

Text Solution

Verified by Experts

The correct Answer is:
D
As, `v=sqrt((2gh)/(1+K^(2)//R^(2)))`
Given, `h=(\3v^(2))/(4g)rArrv^(2)=(2gh)/(1+(K^(2))/(R^(2)))=(2g 3v^(2))/(4g(1+(K^(2))/(R^(2))))=(6gv^(2))/(4g(1+(K^(2))/(R^(2))))`
`1=(3)/(2(1+K^(2)//R^(2)))\or1+(K^(2))/(R^(2))=(3)/(2)`
or `(K^(2))/(R^(2))=(3)/(2)-1=(1)/(2)rArrK^(2)=(1)/(2)R^(2)` (Equation of disc)
Hence, the object is disc.
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