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A block of mass is placed on a surface w...

A block of mass is placed on a surface with a vertical cross section given by `y=x^3/6`. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

A

`(1)/(6)m`

B

`(2)/(3)m`

C

`(1)/(3)m`

D

`(1)/(2)m`

Text Solution

Verified by Experts

The correct Answer is:
A
At limiting equailibrium,
`mu= tan theta`
`tan theta= mu=(dy)/(dx)=(x^(2))/(2)` (from questions)
`:.` Coefficieint of friction `mu=0.5`
`:. 0.5 =(x^(2))/(2) rArr x=+1`
Now , `y=(x^(3))/(6)=(1)/(6)m`
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