Question

A block is lying on an inclined plane which makes ${60}^o$ with the horizontal . If coefficient of friction between block and plane is 0.25 and $g=10m/s^2$, then acceleration of the block when it moves along the plane will be

• A. $2.50m/s^2$
• B. $5.00m/s^2$
• C. $7.4m/s^2$
• D. $8.66m/s^2$

Answer 1

The correct option is C $7.4m/s^2$

Given that,

Coefficient of friction $\mu =0.25$

Angle $\theta ={60}^0$

Now, weight of the block

$W=mg\sin \theta$

Now, the friction force

$F=\mu mg\cos \theta$

Now, the net force of the block

$F=ma$

$ma=mg(\sin \theta -\mu \cos \theta )$

$a=10\times \frac{\sqrt{3}}{2}-0.25\times 10\times \frac{1}{2}$

$a=5\sqrt{3}-1.25$

$a=7.4m/s^2$

Hence, the acceleration of the block is $7.4m/s^2$