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A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.?
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A disc of mass m and radius 1 m is hinged at its centre on a frictionl...
- Given data
- Mass of disc (m) = m
- Radius of disc (r) = 1 m
- Mass of small particle = m/2
- Initial velocity of particle = 10 m/s
- Coefficient of friction between particle and disc (µ) = 0.5
- Analysis
- The small particle is projected with velocity 10 m/s and is in contact with the wall and base of the disc.
- The frictional force between the particle and the disc will provide the necessary centripetal force for the circular motion.
- The particle will move in a circular path due to the centripetal force acting towards the center of the disc.
- The angular displacement of the disc can be calculated using the equation for circular motion.
- Calculation
- The frictional force acting on the particle = µ * Normal force
- Normal force = mg + mv²/r (centripetal force)
- For circular motion, mv²/r = µ * (mg + mv²/r)
- Solving for v, we get v = √(µrg/(1 - µ))
- Substituting the values, v = √(0.5 * 10 * 1 / (1 - 0.5)) = 5√2 m/s
- Angular velocity (ω) = v/r = 5√2 rad/s
- Angular displacement (θ) = ω * t = 5√2 * 2 = 10√2 rad
- Conclusion
After 2 seconds, the angular displacement of the mass will be 10√2 radians. The particle will continue to move along the circular path with the given velocity and maintain contact with the wall and base of the disc due to the frictional force acting between them.
- Mass of disc (m) = m
- Radius of disc (r) = 1 m
- Mass of small particle = m/2
- Initial velocity of particle = 10 m/s
- Coefficient of friction between particle and disc (µ) = 0.5
- Analysis
- The small particle is projected with velocity 10 m/s and is in contact with the wall and base of the disc.
- The frictional force between the particle and the disc will provide the necessary centripetal force for the circular motion.
- The particle will move in a circular path due to the centripetal force acting towards the center of the disc.
- The angular displacement of the disc can be calculated using the equation for circular motion.
- Calculation
- The frictional force acting on the particle = µ * Normal force
- Normal force = mg + mv²/r (centripetal force)
- For circular motion, mv²/r = µ * (mg + mv²/r)
- Solving for v, we get v = √(µrg/(1 - µ))
- Substituting the values, v = √(0.5 * 10 * 1 / (1 - 0.5)) = 5√2 m/s
- Angular velocity (ω) = v/r = 5√2 rad/s
- Angular displacement (θ) = ω * t = 5√2 * 2 = 10√2 rad
- Conclusion
After 2 seconds, the angular displacement of the mass will be 10√2 radians. The particle will continue to move along the circular path with the given velocity and maintain contact with the wall and base of the disc due to the frictional force acting between them.
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A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.?
Question Description
A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.?.
A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc of mass m and radius 1 m is hinged at its centre on a frictionless horizontal surface. It has a massless wall of short height around the circumference. A small particle of mass m/2 is projected with velocity 10 m/s keeping it in contact with the wall and base of the disc. If coefficient of friction between the small particle and the base of the disc in 0.5 and the wall is smooth. Find the angular displacement of the mass after 2 sec.?.
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