Question

Two identical blocks $A$ and $B$ are placed on two inclined planes as shown in the figure. Neglect resistance and other friction.

Read the following statements and choose options.
Statement I : The kinetic energy of $A$ on sliding to $J$ will be greater than the kinetic energy of $B$ on sliding to $O$.
Statement II : The acceleration of $A$ will be greater than acceleration of $B$ when both are released on the inclined plane.
Statement III : The work done by external agent to move the block slowly from position $B$ to $O$ is negative.

• A. Only statement I is true
• B. Only statement II is true
• C. Only I and III are true
• D. Only II and III are true

Answer 1

Answer: (D)

Statement I: Work done by gravity is same for motion from $A$ to $J$ and $B$ to $M$ for equal mass. So KE will be equal.
Statement II: Acceleration $=g\sin \theta$
$\sin {\theta }_A>\sin {\theta }_B$
$\Rightarrow \frac{h}{l}>\frac{h}{2l}$
Statement III: $W_g+W_{\text{ext }}=0$ (Because the block moves slowly)
$W_{\text{ext }}=-W_g$
From $B$ to $O:W_g$ is positive, so $W_{\text{ext }}<0$.