Question

A body of mass $2\, kg$ slides down with an acceleration of $3 \, m/s^2$ on a rough inclined plane having a slope of $30^{\circ}$. The external force required to take the same body up the plane with the same acceleration will be : $(g = 10 \, m/s^2)$

• A. 14 N
• B. 20 N
• C. 6 N
• D. 4 N

Answer 1

The Correct Option is B

To find the external force required to take the body up the inclined plane with the same acceleration, we must analyze the forces acting on the body. Here are the steps to solve the problem:

1. The weight of the body acting downwards is given by: \( W = m \times g = 2 \times 10 = 20 \, \text{N} \).
2. The component of the weight acting down the inclined plane is: \( W_{\text{down\_slope}} = W \times \sin 30^{\circ} = 20 \times 0.5 = 10 \, \text{N} \).
3. The frictional force \( f \) acting against the motion while sliding down, can be found using Newton's second law: \( m \cdot a = W_{\text{down\_slope}} - f \) where \( a = 3 \, \text{m/s}^2 \), hence:
   \( 2 \times 3 = 10 - f \rightarrow f = 4 \, \text{N} \)
4. To move the body up the plane with the same acceleration, the external force \( F \) must overcome both the gravitational component acting downslope and the frictional force. Hence, \( F = m \cdot a + W_{\text{down\_slope}} + f \).
5. Substitute the known values:
   \( F = 2 \times 3 + 10 + 4 = 6 + 10 + 4 = 20 \, \text{N} \).

Therefore, the external force required to take the same body up the plane with an acceleration of \( 3 \, \text{m/s}^2 \) is 20 N.