Question

Assertion Force applied on a block moving in one-dimension is producing a constant power, then the motion should be uniformly accelerated.
Reason This constant power multiplied with time is equal to the change in kinetic energy.

• A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Assertion is incorrect but Reason is correct.

Answer 1

Answer: (D)

From work-energy theorem,
$W=\Delta KE=\frac{1}{2}m{v}^2$ ...(i)
The power, $P=\frac{\text{ work done }}{\text{ Time }}=\frac{W}{t}$
$\Rightarrow W=P\times t$ ...(ii)
From Eqs (i) and (ii), we get
$P\times t=\Delta KE=\frac{1}{2}m{v}^2$ ...(iii)
$\therefore$ Power multiplied with time is equal to the change in kinetic energy.
Also, $P=F\cdot v$
From Eq. (iii),
$v^2\propto t$ or $v\propto t^{1/2}$
Differentiating Eq. (iv), we get
$\frac{dv}{dt}\propto t^{-1/2}$
or $a\propto t^{-1/2}$
Thus, the motion is not uniformly accelerating. Therefore, Assertion is incorrect but Reason is correct.