
A $20\,kg$ block is initially at rest on a rough horizontal surface. A horizontal force of $75\,N$ is required to set the block in motion. After it is in motion, a horizontal force of $60\,N$ is required to keep the block moving with constant speed. The coefficient of static friction is
(A) $0.60$
(B) $0.44$
(C) $0.52$
(D) $0.38$
Answer
124.5k+ views
Hint Since the question is asking about the coefficient of static friction, you need to consider the force which is required to change the state of the block from rest to motion. Maximum static friction is nothing but the maximum amount of friction that can act on a body while it is in rest. Hence, to change a body’s state from rest to motion, you need to apply at least the amount of force equal to the maximum static friction.
Complete step by step answer
As explained in the hint section of the solution to the asked question, we need to consider the force which is needed to set the block in motion since the question is only asking us about the coefficient of static friction. The coefficient of static friction is the deciding factor in the maximum amount of friction that can be applied on an object or body which is currently at rest and if someone wants to set the object or the body in motion, they have to apply the amount of force which is at least equal to or more than the maximum static friction that can be applied on the object.
Let us have a look at the relevant information given in the question:
Mass of the block, $m = 20\,kg$
Horizontal force required to set the block in motion, ${f_h} = 75\,N$
Now, since there is no motion in vertical direction, we can safely say that the normal reaction force balances the weight of the block, hence:
$
N = W \\
N = mg \\
N = 20 \times 10 = 200\,N \\
$
Friction is given as:
${f_s} = {\mu _s}N$
Since the force needed to set the block in motion is given, we can write:
${f_s} = {f_h}$
Substituting their values, we get:
$
{\mu _s}\left( {200} \right) = 75 \\
\Rightarrow {\mu _s} = 0.375 \\
\Rightarrow {\mu _s} \approx 0.38 \\
$
As we can see, this matches with the value given in the option (D). Hence, the correct answer is option (D).
Note The main confusion can be the deduction about which of the two given forces we need to use so as to find the value of coefficient of static friction. As we explained that to find the value of coefficient of static friction, we need to consider only the force which needs to set the block in motion from rest.
Complete step by step answer
As explained in the hint section of the solution to the asked question, we need to consider the force which is needed to set the block in motion since the question is only asking us about the coefficient of static friction. The coefficient of static friction is the deciding factor in the maximum amount of friction that can be applied on an object or body which is currently at rest and if someone wants to set the object or the body in motion, they have to apply the amount of force which is at least equal to or more than the maximum static friction that can be applied on the object.
Let us have a look at the relevant information given in the question:
Mass of the block, $m = 20\,kg$
Horizontal force required to set the block in motion, ${f_h} = 75\,N$
Now, since there is no motion in vertical direction, we can safely say that the normal reaction force balances the weight of the block, hence:
$
N = W \\
N = mg \\
N = 20 \times 10 = 200\,N \\
$
Friction is given as:
${f_s} = {\mu _s}N$
Since the force needed to set the block in motion is given, we can write:
${f_s} = {f_h}$
Substituting their values, we get:
$
{\mu _s}\left( {200} \right) = 75 \\
\Rightarrow {\mu _s} = 0.375 \\
\Rightarrow {\mu _s} \approx 0.38 \\
$
As we can see, this matches with the value given in the option (D). Hence, the correct answer is option (D).
Note The main confusion can be the deduction about which of the two given forces we need to use so as to find the value of coefficient of static friction. As we explained that to find the value of coefficient of static friction, we need to consider only the force which needs to set the block in motion from rest.
Recently Updated Pages
Difference Between Circuit Switching and Packet Switching

Difference Between Mass and Weight

JEE Main Participating Colleges 2024 - A Complete List of Top Colleges

JEE Main Maths Paper Pattern 2025 – Marking, Sections & Tips

Sign up for JEE Main 2025 Live Classes - Vedantu

JEE Main 2025 Helpline Numbers - Center Contact, Phone Number, Address

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility & More

Class 11 JEE Main Physics Mock Test 2025

JEE Main Exam Marking Scheme: Detailed Breakdown of Marks and Negative Marking

JEE Main 2023 January 24 Shift 2 Question Paper with Answer Keys & Solutions

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Fluids

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

NCERT Solutions for Class 11 Physics Chapter 7 Gravitation
