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Question
Multiple Choice Question.
Two hailstones with radii in the ratio of 1:4 fall from a great height through the atmosphere. Then the ratio of their terminal velocities is
Options
1:2
1:12
1:16
1:8
Solution
Two hailstones with radii in the ratio of 1:4 fall from a great height through the atmosphere. Then the ratio of their terminal velocities is 1:16
Explanation:
Let r1 and r2 be the radius of two hailstones falling from a great height through atmosphere then:
From question,
`r_1/r_2 = 1/4` .....(i)
We have an expression for the velocity of moving body in the atmosphere as:
`v = 2/9 r^2g (d_2 - d_1)/n`
Where, r, g, d1 and d2 are radius of the body, acceleration due to gravity, the density of the body, density of medium respectively.
Therefore, `v oo r^2`
If v1 and v2 are the velocity of hailstones 1 and 2.
The expression for the ratio of their velocity will be:
`v_1/v_2 = r_1^2/r_2^2`
Thus, from the equation (i)
`v_1/v_2 = r_1^2/r_2^2`
`v_1/v_2 = (r_1/r_2)^2`
`v_1/v_2 = (1/4)^2`
`v_1/v_2 = 1/16`
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