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In the situation shown, the force requir...

In the situation shown, the force required to just move a body up an inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction between the block and plane is `mu`. The angle of inclination of the plane from horizontal is given by :

A

tan `theta = mu`

B

tan `theta = 2 mu`

C

tan `theta = 0.5 mu`

D

tan `theta = 3 mu`

Text Solution

Verified by Experts

The correct Answer is:
D
Force required to just move the body up the inclined plane is `F_(1) = mg sin theta + mu m g cos theta`
Force required to just prevent sliding is `F_(2) = m g sin theta = mu g cos theta`
Given `F_(1) = 2F_(1) implies (m g sin theta + mu m g cos theta) = 2 (m g sin theta - mu m g cos theta)`
`implies tan theta + mu = 2 (tan theta - mu) implies tan theta = 3 mu`
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Knowledge Check

  • The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is mu . If theta is the angle of inclination of the plane than tan theta is equal to

    A
    `mu`
    B
    `3 mu`
    C
    `2 mu`
    D
    `0.5 mu`

  • The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is 60^(@) is

    A
    `(1)/(sqrt2)`
    B
    `(1)/(sqrt3)`
    C
    `(1)/(2)`
    D
    `(1)/(3)`

  • The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is 60^(@) is .

    A
    `(1)/(sqrt2)`
    B
    `(1)/(sqrt3)`
    C
    `(1)/(2)`
    D
    `(1)/(3)`

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