Assertion :An object of mass m is initially at rest. A constant force $F$ acts on it. Then the velocity gained by the object during a fixed displacement is proportional to $1 / \sqrt{m}$ . Reason: For a given constant force and displacement, velocity is always inversely proportional to root of mass.

Statement -1 is false, Statement-2 is true

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Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1

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Statement -1 is true,Statement-2 is true; Statement -2 is not a correct explanation for Statement-1

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Statement -1 is true, Staternent-2 is false

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Solution

The correct option is B Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
Using third equation of motion:
$v^{2} = u^{2} + 2 \times a \times s$ and $F = m \times a$

We get: $v^{2} \propto \frac{F}{m} \times s$ , as $u = 0$

or, $v \propto \sqrt{\frac{F}{m} \times s}$

Hence, for a given force and displacement velocity is always inversely proportional to root of mass, and reason is correct explanation of mass.

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Assertion :An object of mass m is initially at rest. A constant force F acts on it. Then the velocity gained by the object during a fixed displacement is proportional to 1/√m. Reason: For a given constant force and displacement, velocity is always inversely proportional to root of mass.