Can you explain the answer of this question below:The ratio of the heights from which two bodies are dropped is 3:5 respectively. The ratio of their final velocities is:A:9 : 25B:√ 3 : √ 5C:5 : 3D:√5 : √3The answer is b.

Question

Can you explain the answer of this question below:The ratio of the heights from which two bodies are dropped is 3:5 respectively. The ratio of their final velocities is:&#8203;A:9 : 25B:&#8730; 3 : &#8730; 5C:5 : 3D:&#8730;5 : &#8730;3The answer is b.

Answer

3:5
c)5:3
d)25:9

Solution:
The ratio of heights from which the two bodies are dropped is 3:5. Let us assume that the heights are 3x and 5x respectively.

Let u1 and u2 be the initial velocities of the two bodies. We know that the initial velocity of both the bodies is zero. So, u1 = u2 = 0

Let v1 and v2 be the final velocities of the two bodies. We know that the final velocity of a body dropped from a height h is given by v = sqrt(2gh), where g is the acceleration due to gravity.

So, v1 = sqrt(2g*3x) and v2 = sqrt(2g*5x)

Now, we need to find the ratio of their final velocities, which is given by v1/v2.

v1/v2 = (sqrt(2g*3x))/(sqrt(2g*5x))

v1/v2 = sqrt(3x/5x)

v1/v2 = sqrt(3/5)

v1/v2 = 0.7746

v1:v2 = 3:3.8714 (approx)

Therefore, the ratio of their final velocities is approximately 3:3.8714, which can be simplified as 9:25 (approx). Hence, the answer is option (a) 9:25.

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