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  4. A particle falls from rest under gravity. Its potential energy with respect to ground (P E) and its kinetic energy (K E) are plotted against time (t). Choose the correct graph:

Q. A particle falls from rest under gravity. Its potential energy with respect to ground $(P E)$ and its kinetic energy $(K E)$ are plotted against time $(t)$. Choose the correct graph:

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Solution:

As a particle falls its gravitational potential energy decreases and kinetic energy increases with speed given as $v=g t$ so the possible option is (B).

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3. A body constrained to move along Z-axis of a coordinate system is subjected to a constant force $F$ given by $F =-\hat{i ⁡}+2\hat{j ⁡}+3\hat{k}N⁡$ where $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are the unit vector along the X, Y and Z-axis of the system respectively. What is the work done by this force in moving the body a distance of $4 \, m$ along the Z-axis?

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4. A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_{c}$ is varying with time $t$ as $a_{c}=k^{2} \, rt^{2}$ , where $k$ is a constant. The power delivered to the particle by the force acting on it is

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5. A ball of mass $1\, kg$ collides with a wall with speed $8\, ms ^{-1}$ and rebounds on the same line with the same speed. If mass of the wall is taken as infinite, the work done by the ball on the wall is

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