Assertion (A): Two particles start moving with velocities \(vec{v}_1\) and \(vec{v}_2\) respectively in a plane. They can meet only if component of their velocities perpendicular to line joining them are equal.
Reason (R): Relative velocity of a body w.r.t. other body is calculated along the line joining two 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): For particles to meet, their relative perpendicular velocity component must be zero, meaning their perpendicular velocities must be equal. Otherwise, they would move apart perpendicular to the line joining them. So (A) is true.
Reason (R): Relative velocity is a vector difference and can be calculated in any direction, not exclusively along the line joining two bodies. So (R) is false.
Assertion (A): The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank. They may reach opposite bank simultaneously moving along different straight line paths.
Reason (R): For above boats to cross the river in same time, the components of their velocity relative to river in direction normal to flow should be same.
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
The time to cross the river depends on the component of velocity perpendicular to the river flow (\(v_{\text{normal}}\)). For simultaneous crossing, \(v_{\text{normal}}\) must be equal for both boats. If total speed relative to river is same, and \(v_{\text{normal}}\) is same, then the magnitude of the parallel component is also same. Different paths result from different directions of the parallel component. Thus, (A) is true and (R) is true and explains (A).