Question

Assertion: The acceleration of a body down a rough inclined plane is greater than the acceleration due to gravity.
Reason: The body is able to slide on an inclined plane only when its acceleration is greater than acceleration due to gravity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.

Answer 1

Hint:First try to find out the relation between the acceleration of a body sliding down an inclined plane and the acceleration due to gravity. Then after finding the relation check which one that is acceleration of body sliding or acceleration due to gravity is greater and hence get the required result.



Formula used
1. Acceleration of the body, \[a = g\left( {\sin \theta - \cos \theta } \right)\]
Where, g is acceleration due to gravity.
2. Force of body sliding down an inclined plane;
$F = mg\sin \theta - \mu R$
3. Force, F = ma.


Complete answer:

First we need to find out acceleration of body sliding down a rough inclined plane.
We know that the force on that body is given by:
$F = mg\sin \theta - \mu R$
R will be equal to the vertical component of force that is;
$R = mg\cos \theta $
Putting this value, we get;
$ma = mg\sin \theta - \mu mg\cos \theta $
Taking mg common;
$ma = mg\left( {\sin \theta - \mu \cos \theta } \right)$
By solving, we get;
$a = g\left( {\sin \theta - \mu \cos \theta } \right)$
So, it means $a < g$.
Acceleration of body sliding down the inclined plane is less than the acceleration due to gravity.
Therefore, both the Assertion and Reason is wrong.

Hence, the correct answer is Option D.



Note: Be careful about the horizontal and vertical component of the force applied on the body while it is sliding down the inclined plane. For acceleration of the body we need to find the resultant force using these components. Then finally we will get the value of acceleration of the body in terms of acceleration due to gravity.