Question

A block is moving on an inclined plane making an angle ${45}^o$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. If we define $N=10\mu$, then $N$ is:

• A. 10
• B. 5
• C. 50
• D. 100

Answer 1

Answer: (B)

5

Force require to just push up is $F_1$

and force require to just prevent from sliding is $F_2$

and according to question $F_1=3F_2$

$F_1=mgsin\theta +\mu mgcos\theta$

$F_2=mgsin\theta -\mu mgcos\theta$

Now according to the question

$F_1=3F_2$

put values from above equations

$mgsin\theta +\mu mgcos\theta =mgsin\theta -\mu mgcos\theta$

solving these we will get

$\mu =0.5$

$N=10\times \mu =10\times 0.5=5$

hence the value of N=5

So, (B) is a correct answer