Question

A block of mass $1kg$ is projected from the lowest point up along the inclined plane, if $g=10m/s^2$, the retardation experienced by the block is

• A. $\frac{15}{\sqrt{2}}m/s^2$
• B. $\frac{5}{\sqrt{2}}m/s^2$
• C. $\frac{10}{\sqrt{2}}m/s^2$
• D. zero

Answer 1

The correct option is A $\frac{15}{\sqrt{2}}m/s^2$


Let direction of acceleration in downward direction.
Retarding force will be the friction and gravitational force. So,
$f_s=\mu N=\mu mg\cos {45}^0$
$f_{\text{gravitational}}=mg\sin {45}^0$
By balancing the forces
$ma=\mu mg\cos {45}^0+mg\sin {45}^0$
$a=(0.5\times \frac{10}{\sqrt{2}}+\frac{10}{\sqrt{2}})$
$a=\frac{15}{\sqrt{2}}m/s^2$