Question

A constant force acts on a body of mass m1 at rest and produces a velocity 'v' over a displacement 's1'. The same force acts on another body of mass m2 at rest and produces the same velocity. 'v' over a displacement 's2'. The ratio of the displacements s1 : s2 is

Answer 1

Answer:

m₁ : m₂

Explanation:

·------F------->m₁----------S₁--at v------·

·-----F------->m₂-----------------S₂ at v----------·

For mass m₁,

       ⇒ F = m₁a₁

       ⇒ F / m₁ = a₁           ...( 1 )

For mass m₂,

       ⇒ F = m₂a₂

       ⇒ F / m₂ = a₂          ...( 2 )

For mass m₁,

    v^2 = u^2 + 2a₁S₁

    v^2 = 0 + 2a₁S₁

    v^2 = 2a₁S₁          

Similarly for mass m₂, v^2 = 2a₂S₂, since both have same velocity.

     ⇒ 2a₂S₂ = 2a₁S₁

     ⇒ a₂S₂ = a₁S₁

     ⇒ a₂ / a₁ = S₁ / S₂

     ⇒ ( F / m₂ ) / ( F / m₁ ) = S₁ / S₂              { value of a(s) from above }

    ⇒ m₁ : m₂ = S₁ : S₂