Assertion (A): According to the Newton’s third law of motion, the magnitude of the action and reaction force in an action reaction pair is same only in an inertial frame of reference.
Reason (R): Newton’s laws of motion are applicable only in inertial reference frame.
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
Newton's third law of motion (action-reaction pairs) is universally valid, not only in inertial frames. Thus, A is false. While Newton's first and second laws require inertial frames, the third law is more fundamental and applies in all frames. Thus, R is also false.
Assertion (A): A body is lying at rest on a rough horizontal surface. A person accelerating with acceleration \(a\) (where \(a\) is positive constant and \(\hat{i}\) is a unit vector in horizontal direction) observes the body. With respect to him, the block experiences a kinetic friction.
Reason (R): There is relative motion between the block and surface in person’s frame of reference.
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
In the accelerating person's non-inertial frame, a pseudo-force acts on the block. If this pseudo-force causes relative motion, kinetic friction acts. A is true. Kinetic friction by definition arises due to relative motion between surfaces. So, R is true and correctly explains A.
Assertion (A): A block is hanging from spring. Spring force on block and gravitational force on block are not action and reaction pair.
Reason (R): Action and reaction force acts in opposite direction.
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
Action and reaction pairs act on different bodies. Both spring force and gravitational force act on the same block, so they are not an action-reaction pair. Both A and R are true statements, but R does not correctly explain A.
Assertion (A): The acceleration of a body moving down on a rough inclined plane is greater than the acceleration due to gravity.
Reason (R): The body is able to slide on an inclined plane only when its acceleration is greater than acceleration due to 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
Assertion (A) is false. The acceleration of a body on a rough inclined plane is \(a = g(\sin\theta - \mu\cos\theta)\), which is always less than \(g\).
Reason (R) is also false. A body slides when the component of gravity along the plane overcomes static friction, not when its acceleration is greater than \(g\). Thus, both (A) and (R) are false.
Assertion (A): If pseudo force on a body is assumed as action then frictional force may be reaction for this action.
Reason (R): Action-reaction must acts on different bodies.
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 false. Pseudo forces are fictitious and do not constitute action-reaction pairs with real forces like friction, as they are not interaction forces.
Reason (R) is true. According to Newton's third law, action and reaction forces always act on different bodies. Since (A) is false and (R) is true, and no option directly reflects this, the closest option, given (A) is false, is (4), implying both are false, despite (R) being true. This indicates a potential flaw in the provided options.
Assertion (A): A man starts walking towards west. Friction force on him acts towards east.
Reason (R): Friction opposes relative motion.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is false; when walking west, the static friction force on the man acts west, in the direction of motion. Reason (R) is true as friction fundamentally opposes relative motion. Thus, (A) is false and (R) is true. Option (4) is selected as it correctly identifies (A) as false.
Assertion (A): If a particle is found to be in equilibrium in two different frames of reference implies that both frames are inertial.
Reason (R): Newton’s second law can be used for motion of a particle in any reference frame.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is false. Two non-inertial frames accelerating identically relative to an inertial frame could both observe a particle in equilibrium. Reason (R) is false. Newton's second law \( \vec{F} = m \vec{a} \) strictly applies in inertial frames; pseudo forces must be included in non-inertial frames. Therefore, both (A) and (R) are false.
Assertion (A): A rocket moves forward by pushing the surrounding air backward.
Reason (R): There is an equal and opposite reaction to every action.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is false; rockets achieve propulsion by expelling hot gases backward, not by pushing the surrounding air. They work in vacuum. Reason (R) is true, stating Newton's third law. Thus, (A) is false and (R) is true. Option (4) is selected as it correctly identifies (A) as false.
Assertion (A): The apparent weight of a person standing in a lift, which speed up is always greater than his true weight.
Reason (R): The gravity force due to earth always acts downwards.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
If the lift speeds up *upwards*, apparent weight \(N = m(g+a)\), which is greater than true weight \(mg\). Under this interpretation, (A) is true. Gravity always acts downwards, so (R) is true. However, (R) does not explain the change in apparent weight due to acceleration.
Assertion (A): An air tight cage in which a bird is sitting, is suspended from a spring balance. If the bird starts flying upwards with some acceleration, then the reading of the balance will increase.
Reason (R): The weighing machine measures the actual weight of a body.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
When the bird flies up with acceleration, it pushes more air downwards, increasing the effective weight measured. So (A) is true. A weighing machine measures apparent weight, not always actual weight. Thus (R) is false.