Q. 414.7( 3 Votes )

# A car is speeding up on a horizontal road with an acceleration a. Consider the following situations in the car. (i) A ball is suspended from the ceiling through a string and is maintaining a constant angle with the vertical. Find this angle. (ii) A block is kept on a smooth incline and does not slip on the incline. Find the angle of the incline with the horizontal.

Answer :

Given: Let the pendulum (formed by the ball and the string) make angle θ with the vertical.

From the free-body diagram, Tcosθ − mg = 0

Tcosθ = mg

…i

ma − T sin θ = 0

⇒ ma = T sin θ

…. ii

So, the angle formed by the ball with the vertical is tan⁻ �[ a/g.]

(ii) Let the angle of the incline be θ. From the diagram,

⇒ ma cos θ = mg sin θ

So, the angle of incline is tan⁻ �(a/g)

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PREVIOUSA block A can slide on a frictionless incline of angle θ and length l, kept inside an elevator going up with uniform velocity u (figure 5-E22). Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline.NEXTA block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s2. Find the displacement of the block during the first 0.2 s after the start. Take g = 10 m/s2.

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