devarshi-dt-logo

Question:

The machine as shown has 2 rods of length 1m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a:

Decreasing speed

Constant speed

Increasing speed speed which is34thof the

Roller when weight is0.4mabove the ground

Solution:

⇒dy/dt=Vc
Let the speed of the roller at A be VA
⇒dx/dt=VA
Also, sinθ=y/1, cosθ=x/2
differentiating with respect to time
⇒-cosθdθ/dt=Vc/2, sinθdθ/dt=VA/2
⇒Vc=VA/2tanθ
as A moves towards right, θ increases, hence Vc decreases.
So, option D