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Second Law of Motion

A constant fo...

Question

A constant force acts on a body of mass $m_{1}$ which is at rest and produces a velocity 'v' over a displacement $s_{1}$ . The same force acts on another body of mass $m_{2}$ at rest and produces the same velocity 'v' over a displacement $s_{2}$ . The ratio of the displacements, $s_{1} : s_{2}$ is

m_{1} : m_{2}

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m_{2} : m_{1}

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\sqrt{m_{1}} : \sqrt{m_{2}}

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\sqrt{m_{2}} : \sqrt{m_{1}}

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Solution

The correct option is B $m_{1} : m_{2}$
The acceleration of the first body, $a_{1} = \frac{F}{m_{1}}$
The acceleration of the second body, $a_{2} = \frac{F}{m_{2}}$
We know that, $v^{2} = 2 a s$
$\Rightarrow 2 \times \frac{F}{m_{1}} \times s_{1} = v^{2} = 2 \times \frac{F}{m_{2}} \times s_{2}$
$\Rightarrow 2 \times \frac{F}{m_{1}} \times s_{1} = 2 \times \frac{F}{m_{1}} \times s_{2}$
$\Rightarrow \frac{s_{1}}{s_{2}} = \frac{m_{1}}{m_{2}}$

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A constant force acts on a body of mass m1 which is 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

The correct option is B m1:m2The acceleration of the first body, a1=Fm1The acceleration of the second body, a2=Fm2We know that, v2=2as⇒2×Fm1×s1=v2=2×Fm2×s2⇒2×Fm1×s1=2×Fm1×s2⇒s1s2=m1m2

A constant force acts on a body of mass $m_{1}$ which is at rest and produces a velocity 'v' over a displacement $s_{1}$ . The same force acts on another body of mass $m_{2}$ at rest and produces the same velocity 'v' over a displacement $s_{2}$ . The ratio of the displacements, $s_{1} : s_{2}$ is