Rotational Motion

Step 1: Write the dimensions of the given constants:
Step 2: Assume the required time is proportional to:
Step 3: Substitute dimensions:
Step 4: Equate powers of , , and : For mass : For length : For time :
Step 5: Substitute and solve:
Step 6: Hence,

Step 1: M.I. of one sphere about its own centre:
Step 2: Shift to axis through side using parallel axis theorem. Two spheres lie at distance ; two at distance .
Step 3:
Step 4: Total mass . Converting: Hence option (B).

Step 1: Understand the concept of acceleration. Acceleration is the rate of change of velocity. It can occur due to a change in speed, direction, or both. Step 2: Analyze the situation. The car is moving north. When brakes are applied, the car slows down. Step 3: Determine the direction of acceleration. When an object slows down, its acceleration is opposite to the direction of motion. Since the car’s velocity is towards the north, the acceleration must be towards the south. Step 4: Evaluate the options.

(A) Incorrect — there is acceleration (deceleration)
(B) Correct — acceleration is southward ✔
(C) Incorrect — that would increase speed
(D) Incorrect — no change in direction
Step 5: Final conclusion. The correct answer is .