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Consider the expression $\int \frac{v \times d v}{g - b v^{2}} = a$ , in which v and g are speed and acceleration due to gravity respectively. What is the dimensional formula of ‘a’.

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L−1

T−2

T−1L−2

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detailed solution

Correct option is C

Given Expression ∫vdvg−bv2=aWhere v=Speed= LT−1g= acceleration due to gravity= LT−2According to principle of homogenity g-bv2 will have the dimensions of acceleration due to gravity.Dimensionally[a]=V2[g]=LT−12LT−2=L

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Consider the expression ∫v×dvg−bv2=a, in which v and g are speed and acceleration due to gravity respectively. What is the dimensional formula of ‘a’.

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Consider the expression $\int \frac{v \times d v}{g - b v^{2}} = a$ , in which v and g are speed and acceleration due to gravity respectively. What is the dimensional formula of ‘a’.