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. lf we define $N=10\mu$, then $N$ is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (D)

5

From figure:
$F_1=mg(sin\theta -\mu cos\theta )$
$F_2=mg(sin\theta +\mu cos\theta )$

Given,
$F_2=3F_1$ .
$\therefore sin\theta +\mu cos\theta =3sin\theta -3\mu cos\theta$
$\therefore \mu =\frac{tan\theta }{2}=\frac{tan{45}^o}{2}=\frac{1}{2}$
$\therefore N=10\mu =5N$