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Q1. A diver in a swimming pool bends his head before diving. Why?

a) Increases his linear velocity

b) Decreases his angular velocity

c) Increases his moment of inertia

d) Decreases his moment of inertia

Concept: Conservation of angular momentum
L = Iω = constant
When the diver bends his head, his mass comes closer to the axis of rotation. Hence, moment of inertia decreases. To conserve angular momentum, angular velocity increases.
Correct Answer: (d) Decreases his moment of inertia
Q2. The angular momentum of a system of particles is conserved when

a) No external force acts

b) No external torque acts

c) No external impulse acts

d) Axis of rotation remains same

Angular momentum changes only if external torque is applied.
τ = dL/dt
If external torque is zero, angular momentum remains constant.
Correct Answer: (b) No external torque acts
Q3. A stone tied to a string breaks while being whirled because

a) Gravitational force is greater

b) Required centripetal force exceeds string tension

c) Required force is less than tension

d) Weight is greater than centripetal force

Centripetal force required:
F = mv² / r
As speed increases, required force increases. When this force exceeds maximum tension the string can sustain, it breaks.
Correct Answer: (b)
Q4. Moment of inertia of a circular loop about an axis at distance R/2

a) ½ MR²

b) ¾ MR²

c) MR²

d) 2 MR²

MI about diameter:
I₀ = ½ MR²
Using parallel axis theorem:
I = I₀ + Md² = ½ MR² + M(R/2)² = ¾ MR²
Correct Answer: (b) ¾ MR²
Q5. A 500 kg car turns with radius 50 m at 36 km/h. Find centripetal force.
Convert speed:
36 km/h = 10 m/s
Apply formula:
F = mv²/r = (500 × 10²)/50 = 1000 N
Correct Answer: (c) 1000 N
Q6. Cyclist inclination while taking a turn
tanθ = v² / rg
Substituting values gives:
tanθ = 1 → θ ≈ 60°
Correct Answer: (c) 60°
Q7. Tension in string rotating with frequency 2/π rev/s
Angular velocity:
ω = 2πf = 4 rad/s
Tension:
T = mω²l = 16ml
Correct Answer: (d) 16ml
Q8. Insect walks on water due to
Answer: Surface Tension
Q9. Water droplets are spherical due to
Answer: Surface Tension
Q10. Surface tension at critical temperature
Answer: Zero
Q11. Unit of coefficient of viscosity
Answer: Ns/m²
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