Q.

The relation tan θ=v2/rg gives the angle of banking of the cyclist going round the curve. Here v is the speed of the cyclist, r is the radius of the curve, and g is the acceleration due to gravity. Which of the following statements about the relation is true?

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a

It is both dimensionally as well as numerically correct.

b

It is neither dimensionally correct nor numerically correct.

c

It is dimensionally correct but not numerically.

d

It is numerically correct but not dimensionally.

answer is A.

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Detailed Solution

Here, [tan⁡θ]=v2rg=M0L0T0. Also, in actual expression for the angle of banking of a road, there is no numerical factor involved. Therefore, the relation is both numerically and dimensionally correct.
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The relation tan θ=v2/rg gives the angle of banking of the cyclist going round the curve. Here v is the speed of the cyclist, r is the radius of the curve, and g is the acceleration due to gravity. Which of the following statements about the relation is true?