Relative Velocity — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Relative Velocity MCQs with step-by-step solutions (21 questions). Part of Motion in a Plane (Std 11). Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Relative Velocity · easy · theory
The relative velocity of body $A$ with respect to body $B$ is given by:
A. $\vec{v}_A - \vec{v}_B$ ✓ Correct
B. $\vec{v}_B - \vec{v}_A$
C. $\vec{v}_A\cdot\vec{v}_B$
D. $\vec{v}_A + \vec{v}_B$
Solution: It is the velocity $A$ appears to have to an observer moving with $B$.
Q2 — Relative Velocity · easy · theory
For two bodies moving in the same direction, the magnitude of their relative velocity is:
A. Always zero
B. The sum of their speeds
C. The difference of their speeds ✓ Correct
D. The product of their speeds
Solution: This is why a train alongside another moving at the same speed appears at rest.
Q3 — Relative Velocity · easy · theory
For two bodies moving in opposite directions, the magnitude of their relative velocity is:
A. The difference of their speeds
B. Zero
C. The product of their speeds
D. The sum of their speeds ✓ Correct
Solution: Their separation changes at the combined rate, which is why oncoming traffic seems to rush past.
Q4 — Relative Velocity · medium · theory
A man walking in the rain must tilt his umbrella forward because:
A. The rain actually changes direction
B. The umbrella is lighter that way
C. The rain appears to fall obliquely in his frame of reference ✓ Correct
D. The wind always blows forward
Solution: The rain velocity relative to the man is the vector difference of the rain and man velocities.
Q5 — Relative Velocity · hard · theory
To cross a river in the shortest time, a boat should be steered:
A. Directly against the current
B. Perpendicular to the bank, regardless of the current ✓ Correct
C. Upstream at an angle
D. Downstream at an angle
Solution: The crossing time depends only on the component of velocity across the river.
Q6 — Relative Velocity · hard · theory
To cross a river by the shortest path, a boat should be steered:
A. Parallel to the bank
B. Upstream at an angle so that the drift is cancelled ✓ Correct
C. Downstream at an angle
D. Perpendicular to the bank
Solution: The upstream component must exactly balance the current for the resultant to be straight across.
Q7 — Relative Velocity · medium · theory
Relative velocity is frame dependent, which means that:
A. It is always zero
B. It has no direction
C. Its value depends on the observer chosen ✓ Correct
D. It is the same for all observers
Solution: A passenger sees the seats as stationary while a person on the platform sees them rushing past.
Q8 — Relative Velocity · medium · theory
Two bodies have zero relative velocity. This means they:
A. Move in opposite directions at equal speeds
B. Are both at rest
C. Move with equal velocities in the same direction ✓ Correct
D. Have equal speeds in any directions
Solution: Equal velocity vectors give $\vec{v}_A - \vec{v}_B = 0$.
Q9 — Relative Velocity · easy · numerical
Two cars move in the same direction at $60\text{ km/h}$ and $40\text{ km/h}$. Their relative speed is:
A. $100\text{ km/h}$
B. $20\text{ km/h}$ ✓ Correct
C. $50\text{ km/h}$
D. $2400\text{ km/h}$
Solution: Same direction means the speeds subtract: $60 - 40 = 20\text{ km/h}$.
Q10 — Relative Velocity · easy · numerical
Two cars move in opposite directions at $60\text{ km/h}$ and $40\text{ km/h}$. Their relative speed is:
A. $2400\text{ km/h}$
B. $100\text{ km/h}$ ✓ Correct
C. $50\text{ km/h}$
D. $20\text{ km/h}$
Solution: Opposite directions means the speeds add.
Q11 — Relative Velocity · hard · numerical
Rain falls vertically at $10\text{ m/s}$ and a man walks at $10\text{ m/s}$. He should hold his umbrella at an angle to the vertical of:
A. $45^\circ$ ✓ Correct
B. $90^\circ$
C. $30^\circ$
D. $60^\circ$
Solution: $\tan\theta = \dfrac{v_{man}}{v_{rain}} = \dfrac{10}{10} = 1$, so $\theta = 45^\circ$.
Q12 — Relative Velocity · medium · numerical
Rain falls vertically at $20\text{ m/s}$ and a man runs at $20\text{ m/s}$. The angle at which he must tilt his umbrella from the vertical is:
A. $30^\circ$
B. $0^\circ$
C. $60^\circ$
D. $45^\circ$ ✓ Correct
Solution: Equal magnitudes again give $\tan\theta = 1$.
Q13 — Relative Velocity · hard · numerical
A boat heads straight across a river at $5\text{ m/s}$ while the current flows at $3\text{ m/s}$. Its resultant speed is approximately:
A. $8\text{ m/s}$
B. $4\text{ m/s}$
C. $2\text{ m/s}$
D. $5.83\text{ m/s}$ ✓ Correct
Solution: The two velocities are perpendicular: $\sqrt{25 + 9} = \sqrt{34} \approx 5.83\text{ m/s}$.
Q14 — Relative Velocity · medium · numerical
A river is $100\text{ m}$ wide and a boat heads straight across at $5\text{ m/s}$. The time to cross is:
A. $10\text{ s}$
B. $50\text{ s}$
C. $20\text{ s}$ ✓ Correct
D. $25\text{ s}$
Solution: Crossing time depends only on the across-river component: $\dfrac{100}{5} = 20\text{ s}$.
Q15 — Relative Velocity · hard · numerical
For the boat of the previous type (crossing in $20\text{ s}$ with a $3\text{ m/s}$ current), the drift downstream is:
A. $100\text{ m}$
B. $60\text{ m}$ ✓ Correct
C. $30\text{ m}$
D. $15\text{ m}$
Solution: Drift $= 3 \times 20 = 60\text{ m}$.
Q16 — Relative Velocity · hard · numerical
Two trains of lengths $100\text{ m}$ and $150\text{ m}$ move in opposite directions at $20\text{ m/s}$ and $30\text{ m/s}$. The time they take to cross each other is:
A. $2.5\text{ s}$
B. $5\text{ s}$ ✓ Correct
C. $25\text{ s}$
D. $10\text{ s}$
Solution: Relative speed $= 50\text{ m/s}$ and total length $= 250\text{ m}$, so $t = \dfrac{250}{50} = 5\text{ s}$.
Q17 — Relative Velocity · easy · numerical
A man walks at $5\text{ m/s}$ and a bus moves in the same direction at $15\text{ m/s}$. The velocity of the bus relative to the man is:
A. $3\text{ m/s}$
B. $10\text{ m/s}$ ✓ Correct
C. $75\text{ m/s}$
D. $20\text{ m/s}$
Solution: $v_{bus} - v_{man} = 15 - 5 = 10\text{ m/s}$.
Q18 — Relative Velocity · easy · numerical
Two trains move towards each other at $30\text{ m/s}$ and $20\text{ m/s}$. Their relative speed is:
A. $600\text{ m/s}$
B. $10\text{ m/s}$
C. $50\text{ m/s}$ ✓ Correct
D. $25\text{ m/s}$
Solution: Approaching bodies have their speeds added.
Q19 — Relative Velocity · medium · numerical
A passenger in a moving train sees the trees outside apparently moving:
A. At twice the speed of the train
B. Forward at the speed of the train
C. Backward at the speed of the train ✓ Correct
D. At rest
Solution: In the train frame the trees have velocity $-\vec{v}_{train}$.
Q20 — Relative Velocity · easy · numerical
Two bodies move with the same velocity in the same direction. The velocity of one relative to the other is:
A. Twice the velocity of either
B. Zero ✓ Correct
C. Perpendicular to their motion
D. Equal to the velocity of either
Solution: $\vec{v}_A - \vec{v}_B = 0$ when the two velocity vectors are identical.
Q21 — Relative Velocity · medium · numerical
A boat can move at $5\text{ m/s}$ in still water. In a river flowing at $3\text{ m/s}$, its maximum speed downstream is:
A. $8\text{ m/s}$ ✓ Correct
B. $5.83\text{ m/s}$
C. $2\text{ m/s}$
D. $5\text{ m/s}$
Solution: Moving with the current the two velocities add directly.