Question

two balls of identical shape and size, but of different materials are acted upon by the same force, such that the acceleration of the first ball is only one fourth that of the second ball. calculate the ratio of the mass of the first ball with respect to that of the second ball ​

Answer 1

Let the First ball be A

And second ball be B

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From Newton's Second law of motion we have :-

$\boxed{\boxed{F=MA}}$

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Now,

Force is both case remains constant.

Acceleration of A = One-fourth of acceleration of B

So,

$Acceleration\:A = \frac{1}{4}\:Acceleration\:B$

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Let acceleration of Ball A be x and Ball be 4x

Case 1 (Ball A)

F=MA

F = Mx

M(1)= F/x

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Case 2 (Ball B)

F =MA

F = 4Mx

M(2) = F/4x

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Ratio of Mass of A to Mass of B will be :-

$= \frac{ \frac{f}{x} }{ \frac{f}{4x} } \\ \\ \\ = \frac{4x}{x} \\ \\ \\ = \frac{4}{1} \\ \\ \boxed{ \boxed{4:1}}$

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