Q155 / 160 · TS EAMCET 2003 · Physics

Consider the following statements $A$ and $B$ identify the correct answer given below : (A) A body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time (B) When a body is at rest, it must be in equilibrium.

  • A
    $A$ and $B$ are correct
  • B
    $A$ and $B$ are wrong
  • Correct answer
    C
    $A$ is correct and $B$ is wrong
  • D
    $A$ is wrong and $B$ is correct

Solution

$\mathrm{KE}=\frac{1}{2} m v^2=\frac{1}{2} m(a t)^2=\frac{1}{2} m a^2 t^2$ Rate of change of KE, $\frac{d K}{d t}=\frac{d}{d t}\left(\frac{1}{2} m a^2 t^2\right)=m a^2 t$ $\therefore \quad \frac{d K}{d t} \propto t$ So, statement $A$ is correct. When the body is at rest, then it may be or may not be in equilibrium, so statement $B$ is wrong.

Hence, the correct answer is option: 'C'.

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