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Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?
- a)Both cylinders P and Q reach the ground at the same time.
- b)Cylinders P has larger linear acceleration than cylinder Q.
- c)Both cylinders reach the ground with same translational kinetic energy.
- d)Cylinder Q reaches the ground with larger angular speed.
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two solid cylinders P and Q of same mass and same radius start rolling...
Explanation:
To understand why option D is correct, let's analyze the motion of both cylinders P and Q.
Initial Conditions:
- Both cylinders start rolling down the inclined plane from the same height.
- They have the same mass and the same radius.
For Cylinder P:
- Most of the mass is concentrated near its surface.
- It has a larger moment of inertia compared to Cylinder Q.
- Due to its larger moment of inertia, it requires more torque to rotate.
- As it rolls down the inclined plane, the torque generated by its mass distribution causes it to rotate at a slower angular speed.
- The rotational kinetic energy of Cylinder P is smaller compared to its translational kinetic energy.
For Cylinder Q:
- Most of the mass is concentrated near its axis.
- It has a smaller moment of inertia compared to Cylinder P.
- Due to its smaller moment of inertia, it requires less torque to rotate.
- As it rolls down the inclined plane, the torque generated by its mass distribution causes it to rotate at a faster angular speed.
- The rotational kinetic energy of Cylinder Q is larger compared to its translational kinetic energy.
Now, let's address each option:
a) Both cylinders P and Q reach the ground at the same time:
- This statement is incorrect because Cylinder P has a larger moment of inertia and therefore rotates at a slower angular speed.
- The time taken to reach the ground will be different for both cylinders.
b) Cylinder P has larger linear acceleration than cylinder Q:
- This statement is incorrect because both cylinders have the same mass and start from the same height.
- Therefore, they will have the same linear acceleration.
c) Both cylinders reach the ground with the same translational kinetic energy:
- This statement is incorrect because the rotational kinetic energy of Cylinder P is smaller compared to its translational kinetic energy, while the rotational kinetic energy of Cylinder Q is larger compared to its translational kinetic energy.
d) Cylinder Q reaches the ground with larger angular speed:
- This statement is correct because Cylinder Q has a smaller moment of inertia and therefore rotates at a faster angular speed compared to Cylinder P.
Therefore, the correct option is D.
To understand why option D is correct, let's analyze the motion of both cylinders P and Q.
Initial Conditions:
- Both cylinders start rolling down the inclined plane from the same height.
- They have the same mass and the same radius.
For Cylinder P:
- Most of the mass is concentrated near its surface.
- It has a larger moment of inertia compared to Cylinder Q.
- Due to its larger moment of inertia, it requires more torque to rotate.
- As it rolls down the inclined plane, the torque generated by its mass distribution causes it to rotate at a slower angular speed.
- The rotational kinetic energy of Cylinder P is smaller compared to its translational kinetic energy.
For Cylinder Q:
- Most of the mass is concentrated near its axis.
- It has a smaller moment of inertia compared to Cylinder P.
- Due to its smaller moment of inertia, it requires less torque to rotate.
- As it rolls down the inclined plane, the torque generated by its mass distribution causes it to rotate at a faster angular speed.
- The rotational kinetic energy of Cylinder Q is larger compared to its translational kinetic energy.
Now, let's address each option:
a) Both cylinders P and Q reach the ground at the same time:
- This statement is incorrect because Cylinder P has a larger moment of inertia and therefore rotates at a slower angular speed.
- The time taken to reach the ground will be different for both cylinders.
b) Cylinder P has larger linear acceleration than cylinder Q:
- This statement is incorrect because both cylinders have the same mass and start from the same height.
- Therefore, they will have the same linear acceleration.
c) Both cylinders reach the ground with the same translational kinetic energy:
- This statement is incorrect because the rotational kinetic energy of Cylinder P is smaller compared to its translational kinetic energy, while the rotational kinetic energy of Cylinder Q is larger compared to its translational kinetic energy.
d) Cylinder Q reaches the ground with larger angular speed:
- This statement is correct because Cylinder Q has a smaller moment of inertia and therefore rotates at a faster angular speed compared to Cylinder P.
Therefore, the correct option is D.
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Community Answer
Two solid cylinders P and Q of same mass and same radius start rolling...
A=g sintheta × MR^2 / MR^2 + I ....
so a is inversely proportional to moment of inertia I ....
mass of P is concentrated at the surface so it's moment of inertia is more and mass of Q is near the axis so it's moment of inertia is less... so the body with less moment of inertia will have more acceleration as the relationship is inverse... so the body Q will have more acceleration and will reach the bottom with greater angular speed.. so the option D is correct..
so a is inversely proportional to moment of inertia I ....
mass of P is concentrated at the surface so it's moment of inertia is more and mass of Q is near the axis so it's moment of inertia is less... so the body with less moment of inertia will have more acceleration as the relationship is inverse... so the body Q will have more acceleration and will reach the bottom with greater angular speed.. so the option D is correct..
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Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer?
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Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer?.
Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclinedplane from the same height at the same time. Cylinder P has most of its mass concentrated nearits surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are)correct?a)Both cylinders P and Q reach the ground at the same time.b)Cylinders P has larger linear acceleration than cylinder Q.c)Both cylinders reach the ground with same translational kinetic energy.d)Cylinder Q reaches the ground with larger angular speed.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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