
The upper half of an inclined plane of inclination is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by.
Answer
522.3k+ views
Hint: Apply Newton’s law of motion separately for both the motions. Final velocity of the first half will be equal to initial velocity of the second half. Magnitude of displacement for both the motions is the same. As we are not asked about time, Newton’s third law of motion will be helpful.
Complete Step By Step Solution:
Let us assume mass of block be m kg, g be acceleration due to gravity, total length of incline l and velocity at halfway v. free body diagram of the block for first half,
The acceleration of block will be along the incline and equal to
As the acceleration is constant for the motion we can apply Newton’s law of motion
Applying Newton’s third law of motion form starting to before reaching rough surface
… (1)
Now, free body diagram of the block for second half
Here as the block is moving only along the incline, net force perpendicular to it must be zero. So,
Also the block is sliding over incline, so friction will be
Acceleration of block will b along the incline will be
As the acceleration is constant for the motion we can apply Newton’s law of motion
Applying Newton’s third law of motion form starting of rough surface to bottom
Putting value of from equation 2 and solving we get
Hence the correct option is A.
Note: This question can be solved with the following method. We know that both half motions are almost identical as initial velocity and final velocity has just got interchanged and length of both motions is the same too. So, we can say the magnitude of acceleration of both should be the same and the direction of acceleration of both should be opposite. So, we will get
.
Complete Step By Step Solution:
Let us assume mass of block be m kg, g be acceleration due to gravity, total length of incline l and velocity at halfway v. free body diagram of the block for first half,

The acceleration of block will be along the incline and equal to
As the acceleration is constant for the motion we can apply Newton’s law of motion
Applying Newton’s third law of motion form starting to before reaching rough surface
Now, free body diagram of the block for second half

Here as the block is moving only along the incline, net force perpendicular to it must be zero. So,
Also the block is sliding over incline, so friction will be
Acceleration of block will b along the incline will be
As the acceleration is constant for the motion we can apply Newton’s law of motion
Applying Newton’s third law of motion form starting of rough surface to bottom
Putting value of
Hence the correct option is A.
Note: This question can be solved with the following method. We know that both half motions are almost identical as initial velocity and final velocity has just got interchanged and length of both motions is the same too. So, we can say the magnitude of acceleration of both should be the same and the direction of acceleration of both should be opposite. So, we will get
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Explain why it is said like that Mock drill is use class 11 social science CBSE

The non protein part of an enzyme is a A Prosthetic class 11 biology CBSE

Which of the following blood vessels in the circulatory class 11 biology CBSE

What is a zygomorphic flower Give example class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

The deoxygenated blood from the hind limbs of the frog class 11 biology CBSE
