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Mathematics

Grade10

Easy

Question

Escape velocity is the velocity at which an object must be travelling to leave a star or planet without falling back to its surface or into orbit. Escape velocity, v, depends on the gravitational constant, G, the mass, M, and radius, r, of the star or planet $straight V space equals space square root of fraction numerator 2 GM over denominator straight r end fraction end root$

Rewrite the equation to solve for mass.

$\frac{({rV}^{2})}{(G)}$
$\frac{({rV}^{2})}{(2 G)}$
$\frac{(V^{2})}{(rG)}$
$\frac{(rV)}{(G)}$

hint Hint:

In this question, we have to find the equation to solve the mass from the equation $straight V space equals space square root of fraction numerator 2 GM over denominator straight r end fraction end root$ velocity (V), depends on the gravitational constant (G), the mass (M), and radius (r) of the star or planet. For this we will have to equate the given equation to find the value of M. Firstly, we will square both the sides to remove the under root sign from the equation, then we cross multiply the equation to the find the value of M. The equation obtained will be the required equation to solve mass.

The correct answer is: $fraction numerator left parenthesis rV squared right parenthesis over denominator left parenthesis 2 straight G right parenthesis end fraction$

$As space per space question comma straight V space equals space square root of fraction numerator 2 GM over denominator straight r end fraction space end root S q u a r i n g space b o t h space s i d e s comma space w e space g e t colon not stretchy rightwards double arrow space straight V squared space equals space open parentheses square root of open fraction numerator 2 GM over denominator straight r end fraction close parentheses squared end root close rightwards double arrow straight V squared space equals space fraction numerator 2 GM over denominator straight r end fraction space C r o s s space m u l t y p l y i n g space t o space g e t space v a l u e space o f space m a s s comma space w e space g e t colon not stretchy rightwards double arrow space straight M space equals space fraction numerator rV squared over denominator 2 straight G end fraction T h e space e q u a t i o n space t o space s o l v e space m a s s space equals fraction numerator rV squared over denominator 2 straight G end fraction.$

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