Question

A wedge moving rightwards has a block of mass 10 kg placed on it. The coefficient of friction between the wedge and the block is 0.8. [take $g=10m{s}^{-2}$]. Select the correct alternative(s) from the following options:

• A. If wedge is moving with constant velocity, then friction acting on the block is 64 N.
• B. If wedge is moving with constant velocity, then acceleration of the block is zero.
• C. If wedge is moving with $a=2\left(\hat{i}\right)m/s^2$, then friction acting on the block is 44 N.
• D. If wedge is moving with $a=10\left(\hat{i}\right)m/s^2$, then friction is 20 N, downward on the wedge along the inclined.

Answer 1

Answer: (B), (C), (D)

The correct options are
B If wedge is moving with $a=2\left(\hat{i}\right)m/s^2$, then friction acting on the block is 44 N.
C If wedge is moving with $a=10\left(\hat{i}\right)m/s^2$, then friction is 20 N, downward on the wedge along the inclined.
D If wedge is moving with constant velocity, then acceleration of the block is zero.

a) If moving with constant velocity then a$=$ 0
so friction available $=\mu mgcos\theta$
$=\left(0.8\right)\left(10\right)\left(10\right)\left(4/5\right)=64N.$
but $mgsin\theta =60N$
so required friction is 60N.
So net force is zero.
c ) $a=2\hat{i}$
$f=mgsin37-macos37=44N$
d) $a=10\hat{i}$
$f=mgsin37-macos37=-20N$
negative sign shows downward on the wedge