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In the adjacent figure, x-axis has been ...

In the adjacent figure, x-axis has been taken down the inclined plane. The coefficient of friction varies with `x` as `mu=kx`, where `k= tan theta`. A block is released at `O`.

The maximum velocity of block will be:

A

`sqrt(g)`

B

`sqrt(g sin theta)`

C

`sqrt(g cos theta)`

D

`sqrt(g tan theta)`

Text Solution

Verified by Experts

The correct Answer is:
B
At any position `= g(sin theta-k x cos theta)`
`a = g sin theta (1-x) (v dv)/(d x) = g sin theta(1-x)`
`rArr overset(v)underset(0)(int)vdv = overset(x)underset(0)(int)g sin(1-x)dx (v^(2))/(2) = g sin theta (x -(x^(2))/(2))`
`v` will max when `a = 0 rArr x = 1 v_(max) = sqrt(gsintheta)`
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Knowledge Check

  • In the adjacent figure, x-axis has been taken down the inclined plane. The coefficient of friction varies with x as mu=kx , where k= tan theta . A block is released at O Maximum distance traveled by block:

    A
    `1 m`
    B
    `2 m`
    C
    `3 m`
    D
    `(1)/(2)m`

  • In the adjacent figure, x-axis has been taken down the inclined plane. The coefficient of friction varies with x as mu = kx , where k = tan theta . A block is released at O Maximum distance traveled by the block :

    A
    1 m
    B
    2 m
    C
    3 m
    D
    `(1)/(2)` m

  • In the adjacent figure, x-axis has been taken down the inclined plane. The coefficient of friction varies with x as mu=kx , where k= tan theta . A block is released at O Frictional force acting on the block after it comes to rest:

    A
    `mg sin theta`
    B
    `2 mg sin theta`
    C
    `(mg sin theta)/(2)`
    D
    `2mg cos theta`