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Consider a block sliding down a frictionless inclined plane with acceleration $a$. If we double the mass of the block, what is its acceleration?
(A) $\dfrac{a}{4}$
(B) $\dfrac{a}{2}$
(C) $a$
(D) $2a$
(E) $4a$

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Last updated date: 17th Apr 2024
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Answer
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Hint: The equation which shows the relation between the mass and acceleration is weight or force equation, the weight or force is the product of the mass and acceleration. By using this relation, what happens to the acceleration when the mass is doubled can be determined.
Useful formula
The equation of force is given by,
$F = ma$
Where, $F$ is the force of the object, $m$ is the mass of the object and $a$ is the acceleration of the object.

Complete step by step solution
If the block is in a horizontal plane, the acceleration of the block acts vertically downwards due to gravitational force, then the acceleration of the block due to gravitation is called acceleration due to gravity. But here the block is sliding in the inclined plane, so the acceleration of the block is given by the product of the acceleration due to gravity and the sine component of the angle of inclination. So, the force or weight is written as,
$F = mg\sin \theta \,................\left( 1 \right)$
Where,
$F$ is the force of the object, $m$ is the mass of the object, $g$ is the acceleration due to gravity and $\theta $ is the angle of inclination.
Now,
The equation of force is given by,
$F = ma\,.................\left( 2 \right)$
By comparing the equation (1) and equation (2), then the acceleration is written as,
$a = g\sin \theta \,................\left( 3 \right)$
By equation (3), it is clear that the acceleration of the block in the inclined plane depends only on the acceleration due to gravity and the angle of inclination. It does not depend on the mass of the block. So, the acceleration remains constant when mass is changed.

Hence, the option (C) is the correct answer.

Note: By equation (3), the acceleration in the inclined plane does not depend on the mass of the block. When the mass of the block is doubled the acceleration will remain the same. When the mass of the block is increased or decreased there is no change in acceleration.