Single Choice

A block is placed on a rough horizontal plane. A time dependent horizontal force $$F=kt$$ acts on the block, where $$k$$ is a positive constant. The acceleration-time graph of the block is:

A
B
Correct Answer
C
D

Solution

As the block is placed on a rough surface there will act static friction on it will attain its maximum value. After that the block will start to slide on the surface with acceleration increasing with time (at the rate of $$Km/s^3$$)
(i) FBD of block when it is static $$\left(t \le \dfrac{rmg}{k}\right)$$
$$kt = fs$$
$$a = 0$$

(ii) After it starts sliding $$\left(t > \dfrac{rmg}{k}\right)$$
$$kt - rmg = a$$
$$\dfrac{dq}{dt} = k$$
Option B is correct.

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