An object of mass initially at rest on a smooth horizontal plane starts moving under the action of a force . In the process of its linear motion, the angle (as shown in the figure) between the direction of force and the horizontal varies as where is a

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Solution

Q.
An object of mass $' m'$ initially at rest on a smooth horizontal plane starts moving under the action of a force $F = 2 N$ . In the process of its linear motion, the angle $θ$ (as shown in the figure) between the direction of force and the horizontal varies as $θ = k x,$ where $' k'$ is a constant and $' x'$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $E = \frac{n}{k} \sin θ .$ The value of $' n'$ is ________ . [2023]

Ans.
(2)

$θ = k x$

$W = K E_{f} - K E_{i}$

$d W = F d x$

$W = \int F_{1} d x = \int F \cos k x d x$

$= \frac{2}{k} (\sin k x)$

$∴$ $E = W = \frac{2}{k} \sin k x = \frac{2}{k} \sin θ$

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