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): A block is lying at rest on horizontal rough surface. A person moving with acceleration \(a\) in forward direction will observe a friction force acting on the block.
Reason (R): When there is relative motion between the two surface then only static friction acts between them.
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 an accelerating (non-inertial) frame, a pseudo-force acts on the block, requiring a forward friction force. So, A is true. Static friction acts when there is no relative motion; kinetic friction acts when there is relative motion. Thus, R is false.
Assertion (A): An insect is climbing up a vertical wall with constant speed then the force applied by the wall on the insect is vertically upwards and equal to its weight.
Reason (R): Friction is a self-adjusting force.
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 an insect climbing at constant speed, the upward friction force component from the wall must balance its weight. Static friction is indeed a self-adjusting force. Both A and R are true statements, and R explains why the friction force can adjust to balance the weight.
A frame of reference A is moving rectilinearly and uniformly with a velocity \(\vec{u}\) with respect to an inertial frame B. A body is moving with velocity \(\vec{v}\) and acceleration \(\vec{a}\) in an inertial system B.
Assertion (A): When we use Newtons second Law in frame B we write \( \Sigma \vec{F}_{net} = m\vec{a} \). Now when we use the same in frame A we will write exactly same \(\Sigma \vec{F}_{net}\) and \(\vec{a}\) .
Reason (R): All inertial system are equally suitable for the description of physical phenomenon.
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
Frame A, moving with constant velocity relative to inertial frame B, is also an inertial frame. Newton's second law \( \Sigma \vec{F}_{net} = m\vec{a} \) holds in all inertial frames with the same forces and acceleration. This is because all inertial systems are equally suitable for describing physical phenomena. Both A and R are true, and R explains A.
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): 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.