JEE Advanced · Physics · 6. Work Power Energy

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A small block of mass $1 \mathrm{~kg}$ is released from rest at the top of a rough track. The track is a circular arc of radius $40 \mathrm{~m}$. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point $Q$, as shown in the figure below, is $150 \mathrm{~J}$. (Take the acceleration due to gravity, $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ ).

Question:

The speed of the block when it reaches the point $Q$ is

A ${5 ms}^{- 1}$
B ${10 ms}^{- 1}$
C $10 \sqrt{3} {ms}^{-1}$
D ${20 ms}^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(B) ${10 ms}^{- 1}$

Step-by-step Solution

Detailed explanation

Apply conservation of energy,

∆ P E - W_{f} = ∆ K E

M g R \sin 30 ° - 150 = \frac{1}{2} M v^{2}

M g \frac{R}{2} - 150 = \frac{1}{2} M v^{2} \Rightarrow 1 \times 10 \times 20 - 150 = \frac{1}{2} \times 1 \times v^{2} \Rightarrow v = 10 m s^{- 1}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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