Question

A force of 150N produces an acceleration of $2m{s^{ - 2}}$ in a body and a force of 200N produces an acceleration of $3m{s^{ - 2}}$. The mass of the body and the coefficient of kinetic friction are
A. 50kg;0.1
B. 25kg;0.1
C. 50kg;0.5
D. 50kg;0.2

Answer 1

Hint: Friction: Friction force is a force which works opposite of applied force. In which friction is working between two surfaces, sliding or rolling. There are two types of friction:
A. Static friction
B. Kinetic friction

Complete step by step answer:
Kinetic friction: The friction which is work on moving objects is known as kinetic friction.
Given in question,
 \[{F_1} = 150N\]
\[{a_1} = 2m{s^{ - 2}}\]
\[{F_2} = 200N\]
\[{a_2} = 3m{s^{ - 2}}\]
\[g = 10m{s^{ - 2}}\]
Find,
m= ?
$\mu $=?
According newton's second law with friction,
$ma = F - \mu mg$ …(1)
Put the value in equation 1,
$m \times 2 = 150 - 10\mu m$ …(2)
$m \times 3 = 200 - 10\mu m$ …(3)
Subtracting equation 2 from equation 3
\[
  m \times 3 = 200 - 10\mu m \\
  \underline {m \times 2 = 150 - 10\mu m} \\
  m = 50 \\
 \]
Put the value of $m = 50$ in equation 2
$50 \times 3 = 200 - 10 \times 50\mu $
$500\mu = 200 - 150$
$500\mu = 50$
$\mu = \dfrac{{50}}{{500}}$
$\mu = 0.1$

So, the correct answer is “Option A”.

Note: Static friction is working on the object which is on rest while the kinetic friction is working on motion. Friction is equal and opposite of applied force.