Question

The expression for downward acceleration of a body on an inclined plane of coefficient of friiction m
and q inclination is
1 )g(sinq+m) 2)gsin theta(1+m) 3) g(sin theta+mcos theta) 4) g(sin theta -mcos theta)​

Answer 1

Explanation:

Answer: g(sin theta - mcos Theta)

Answer 2

Correct Question

The expression for downward acceleration of a body on an inclined plane of coefficient of friction m and  inclination is $\theta$.

1 )g(sinq+m) 2)gsin theta(1+m) 3) g(sin theta+mcos theta) 4) g(sin theta -mcos theta)​.

Answer:

The expression for downward acceleration of a bod yon an inclined plane of coefficient of friction m and q inclination  is $g(sin\theta-mcos\theta)$ and option (4) is correct.

Explanation:

Given:

A body on an inclined plane of coefficient of friction m and q inclination.

To Find:

The expression for downward acceleration of a body on an inclined plane of coefficient of friction m and q inclination.

Solution:

As given, a body on an inclined plane of coefficient of friction m and q inclination.

An inclined plane of coefficient of friction= m

An inclined plane of inclination = $\theta$

Let a body of mass p is placed on an inclined plane of inclination $\theta$ .

The forces acting on the body are:

(1) The weight pg of the body.

(2) Normal force due to incline, N.

3) Limiting frictional force m N.

There will be two components of pg. These are $pg\cos\theta$ perpendicular to the plane and $pg\sin\theta$ parallel (downward ) to the plane.

For the body to remain on the plane , N must be reaction to pg cos (theta).

 $pg\cos\theta=N$  -------- equation no.01.

Let acceleration of the body is a.

The equation of motion of the body  will be:

$pa=pg sin \theta - mN$

Putting the value of N from equation no.01.

$pa=pg sin \theta - m\times pg\cos\theta$

$pa=pg( sin \theta - m\cos\theta)$

$a=g( sin \theta - m\cos\theta)$

Thus,the expression for downward acceleration of a bod yon an inclined plane of coefficient of friction m and q inclination  is $g(sin\theta-mcos\theta)$ and option (4) is correct.

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