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In the figure shown, a spring of spring ...

In the figure shown, a spring of spring constant `K` is fixed at on end and the other end is attached to the mass 'm' . The coefficient of friction between block and the inclined plane is `mu`. The block is released when the spring is in tis natural length. Assuming that the `theta gt mu`, the maximum speed of the block during the motion is.

A

`(cos theta + mu sin theta) g sqrt((m)/(k))`

B

`(cos theta - mu sin theta) g sqrt((m)/(k))`

C

`(sin theta + mu cos theta) g sqrt((m)/(k))`

D

`(sin theta - mu cos theta) g sqrt((m)/(k))`

Text Solution

Verified by Experts

The speed is maximum when acceleration is least
Let displacment of block is `x_(0)` when the speed of block maximum.

At displacement , applying Newton's law to the block along the incline
`mg sin theta = mu mg cos theta + kx_(0)` (1)
Applying work energy theorem to block along and final position is
`k_(f) = k_(i) + mg x_(0) sin theta - (1)/(2) kx_(0)^(2) - mu mg x_(0) cos theta` (2)
Solving (1) and (2) we get,
`V_(max) = (sin theta - mu cos theta) g sqrt((m)/(k))`
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Knowledge Check

  • A block is stationary on an inclined plane If the coefficient of friction between the block and the plane is mu then .

    A
    `mu gttan theta`
    B
    `f =mg sin theta`
    C
    `f = mu mg cos theta`
    D
    the reaction of the ground on the block is mg cos `theta`

  • A block of mass m slides down an inclined plane of inclination theta with uniform speed. The coefficient of friction between the block and the plane is mu . The contact force between the block and the plane is

    A
    mg
    B
    `mg sin theta sqrt(1+mu^(2))`
    C
    `mg sin theta`
    D
    `sqrt((mg sin theta)^(2)+(mumg cos theta)^(2))`

  • A block of mass m slides down an inclined plane of inclination theta with uniform speed The coefficient of friction between the block and the plane is mu . The contact force between the block and the plane is .

    A
    `mg sin thetasqrt(1+mu^(2))`
    B
    `sqrt((mg sin theta)^(2)+(mumgcostheta)^(2))`
    C
    `mg sin theta`
    D
    `mg`

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