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A block of mass m is place on a sm ooth ...

A block of mass m is place on a sm ooth inclined wedge ABC of inclination 0 as shown in figure. The wedge is given an acceleration ‘a’ towards the right. The relation between a and `theta` for the block to rem ain stationary on the wedge is

A

`a =g tan theta`

B

`a=(g)/(cosec theta)`

C

`a= g cos theta`

D

`a=(g)/(sin theta)`

Text Solution

Verified by Experts

The correct Answer is:
A
a = g tan `theta`
System is madeup of

block and slope
Force acting on mass m moving with acceleration a in direction of accceleration = ma
Component of force in direction parallel to slope = ma cos `theta`
Component of weight (W= mg ) in direction parallel to slope =mg sin` theta`
Here block do not move
ma cos `theta = mg sin theta`
`a= g (sin theta )/( cos theta ) = g tan theta`
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