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AIIMS 2018 Physics Circular Motion MCQ Question

Type: MCQ-numerical-Medium-Class 11

A person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of 0.5 m/s at an angle of 120° with the direction of flow of water. The speed of water in the stream is

A

1 m/s

B

0.5 m/s

C

0.25 m/s

D

0.433 m/s

Correct Answer

Option C

Detailed Explanation

Given that vrvm=sin⁡30∘\frac{v_r}{v_m} = \sin 30^\circ and vr=0.25 m/sv_r = 0.25 \, \text{m/s}, we can calculate vmv_m using the sine value: sin⁡30∘=12\sin 30^\circ = \frac{1}{2}. Thus, vr=12vmv_r = \frac{1}{2} v_m leads to vm=2×vr=2×0.25 m/s=0.5 m/sv_m = 2 \times v_r = 2 \times 0.25 \, \text{m/s} = 0.5 \, \text{m/s}. Since the question does not provide specific numerical options, option C is correct based on the calculations, while the other options are not applicable as they do not provide relevant information. This illustrates the relationship between resultant and maximum velocities in a vector context, emphasizing the importance of understanding trigonometric functions in physics.

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