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

A block of mass m 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)/(2)m`

B

`(1)/(6)m`

C

`(2)/(3)m`

D

`(1)/(3)m`

Text Solution

Verified by Experts

The correct Answer is:
b
Here there are six faces
`:. y =(x^(3))/(6)`(vol. of one)
At the point of just sliding `mg sin theta = umg cos theta`
`tan theta=mu,(dy)/(dx) = tan theta=mu=(1)/(2), (x^(2))/(2) =(1)/(2),.y =(x^(3))/(6)`
m.
`:.y=1//6m`
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