Assertion (A): The condition of equilibrium for a rigid body is – Translational equilibrium: \( \sum \vec{F} = 0 \) (i.e. sum of all external forces equal to zero). Rotational equilibrium: \( \sum \vec{\tau} = 0 \) (i.e. sum of all external torques equal to zero.)
Reason (R): A rigid body must be in equilibrium under the action of two equal and opposite forces.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
For rigid body equilibrium, both net force and net torque must be zero. Assertion (A) correctly states this.
Reason (R) is false; two equal and opposite forces can form a couple if not collinear, causing rotation and thus not guaranteeing equilibrium.
Assertion (A): A cyclist always bends inwards while negotiating a curve
Reason (R): By bending he lowers his centre of gravity
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
A cyclist bends inwards to provide the necessary centripetal force and maintain rotational equilibrium by balancing torques. Thus, (A) is true.
Lowering the center of gravity is not the primary reason for bending, making (R) false.
Assertion (A): A ladder is more likely to slip when a person is near the top than when he is near the bottom.
Reason (R): The friction between the ladder and floor decreases as he climbs up.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true; a ladder is more likely to slip when a person is higher up due to increased outward horizontal thrust. Reason (R) is false; the normal force at the base remains constant, so the maximum static friction available does not decrease.
Assertion (A): It is more difficult to open the door by applying the force near the hinge.
Reason (R): Torque is maximum at hinge.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true: Torque \(\tau = rF\sin\theta\) requires a larger force \(F\) for a smaller lever arm \(r\) (near the hinge). Reason (R) is false: Torque is zero at the hinge (pivot point) as \(r=0\). Thus, (A) is true, (R) is false.