System of Particles and Rotational Motion
- A couple produces
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A couple is formed of two equal and opposite forces at some separation; so net force is zero. Hence, a couple does not produce translatory motion; but it causes change in rotational motion.
Correct Option: C
A couple is formed of two equal and opposite forces at some separation; so net force is zero. Hence, a couple does not produce translatory motion; but it causes change in rotational motion.
- A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60º from the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to keep it from slipping. Choose the correct magnitude of the force from the following
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AB is the ladder, let F be the horizontal force and W is the weigth of man. Let N1 and N2 be normal reactions of ground and wall, respectively. Then for vertical equilibrium
W = N1 .....(1)
For horizontal equilibrium, N2 = F .....(2)
Taking moments about A,
N2(AB sin60°) – W(AC cos 60°) = 0 ......(3)
Using (2) and AB = 20 ft, BC = 4 ft, we get
F = 
20 × √3 
= W 20 × 1 pound 2 2 ⇒ F = 8W × 2 = 4W = 150 × 4 pound 20√3 5√3 5√3
= 40√3 = 40 × 1.73 = 69.2 pound
Correct Option: D
AB is the ladder, let F be the horizontal force and W is the weigth of man. Let N1 and N2 be normal reactions of ground and wall, respectively. Then for vertical equilibrium
W = N1 .....(1)
For horizontal equilibrium, N2 = F .....(2)
Taking moments about A,
N2(AB sin60°) – W(AC cos 60°) = 0 ......(3)
Using (2) and AB = 20 ft, BC = 4 ft, we getF = 20 × √3 = W 20 × 1 pound 2 2 ⇒ F = 8W × 2 = 4W = 150 × 4 pound 20√3 5√3 5√3
= 40√3 = 40 × 1.73 = 69.2 pound
- A boy suddenly comes and sits on a circular rotating table. What will remain conserved?
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As net torque applied is zero. Hence,
τ = dL Dt dL = θ, L = constant. Dt
L (angular momentum) remains conserved.Correct Option: B
As net torque applied is zero. Hence,
τ = dL Dt dL = θ, L = constant. Dt
L (angular momentum) remains conserved.
- A disc is rotating with angular velocity ω. If a child sits on it, what is conserved ?
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If external torque is zero, angular momentum remains conserved.
[External torque is zero because the weight of child acts downward]
L = Iω = constantCorrect Option: B
If external torque is zero, angular momentum remains conserved.
[External torque is zero because the weight of child acts downward]
L = Iω = constant
- A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be
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Applying conservation law of angular momentum, I1ω1 = I2ω2
I2 = (Mr²) + 4 (m) (r²) = (M + 4m)r²
(Taking ω1 = ω and ω2 = ω1)
⇒ Mr² ω = (M + 4m)r²ω1Correct Option: C
Applying conservation law of angular momentum, I1ω1 = I2ω2
I2 = (Mr²) + 4 (m) (r²) = (M + 4m)r²
(Taking ω1 = ω and ω2 = ω1)
⇒ Mr² ω = (M + 4m)r²ω1
