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A wheel of radius r and mass m stands in...

A wheel of radius `r` and mass `m` stands in front of a step of height `h`. The least horizontal force which should be applied to the axle of the wheel to allow it to raise onto the step is

A

`(mgh(2r-h))/(r-h)`

B

`mgh(r-h)`

C

`(mg(sqrt(h(2r-h))))/(r-h)`

D

`(mgh)/(r )`

Text Solution

Verified by Experts

The correct Answer is:
C
Applying the condition of rotational equilibrium
`F(r-h)=mgx`
but `r^(2)=x^(2)+(r-h)^(2)impliesx=sqrt(h(2r-h))`
`:. F=(mgsqrt(h(2r-h)))/(r-h)`
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