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A disc is rotating with ω =10rad/s about a fixed central axis which is perpendicular to its plane. The disc has a mass =2kg & radius =10cm. A small particle of mass 100gm is put slowly on the disc’s outer circumference. There is sufficient friction between the disc and the particle. What will be the new angular velocity of the system?

Correct Answer: 9.09 rad/s
The friction acting between the two surfaces will ensure that the particle stays on the disc and doesn’t fly out. The angular momentum of the system will be conserved because there is no external torque. Moment of inertia of disc = MR2/2 = 2*0.01/2 = 0.01kgm2. Moment of inertia with particle on disc = 0.01 + mR2 = 0.01+0.1*0.01 = 0.011kgm2. ∴ I1w1 = I2w2 ∴ 0.01*10 = 0.011*w2 ∴ w2 = 9.09 rad/s.

A disc of radius 10cm is rotating about the central axis perpendicular to its plane. A force of 5N acts on it tangentially. The disc was initially at rest. Calculate the value of power supplied by the force when the disc has rotated by 30°.The mass of the disc is 2kg.

A hollow rod has frictionless inner walls. Inside the rod are two small spheres that are kept on either side of the centre of rod. The rod is rotated about its central axis which is perpendicular to the plane of rotation. If the rod had been rotated by an impulsive torque which gave it an instantaneous angular velocity of 5rad/s, what will be the angular velocity after some finite but long time ‘t’? Assume no external forces act on rod after the impulse. Also state what will happen to the spheres in the centre of the rod. The rod has a mass =2kg & length =10cm. The two spheres have a mass =1kg each.

Each of the following problem has a question and two statements which are labeled 1. and. Use the data given in 1. and 2. to decide whether the statements are sufficient to answer the question.Select one of the following . a.Statements (1) ALONE is sufficient,but (2) ALONE is not sufficient. b.Statements (2) ALONE is sufficient,but (1) ALONE is not sufficient. c. Both statement TOGETHER are sufficient but statement alone is sufficient .How many minutes are there is time period T? (1) Time period T extends from 12.00 midnight to 12.00 noon.(2) Time period T is 2 hours and 180 seconds long.

Each of the following problem has a question and two statements which are labeled 1. and. Use the data given in 1. and 2. to decide whether the statements are sufficient to answer the question.Select one of the following . a.Statements (1) ALONE is sufficient,but (2) ALONE is not sufficient. b.Statements (2) ALONE is sufficient,but (1) ALONE is not sufficient. c. Both statement TOGETHER are sufficient but statement alone is sufficient . A fly crawls around the outside of a circle once.A second fly crawls around the outside of a square once.Which fly travels further ? (1) The diagonal of the square is equal to the diagonal of the circle.(2) The fly crawling around the circle took more time to complete has journey than the fly cawing around the square.

Each of the following problem has a question and two statements which are labeled 1. and. Use the data given in 1. and 2. to decide whether the statements are sufficient to answer the question.Select one of the following . a.Statements (1) ALONE is sufficient,but (2) ALONE is not sufficient. b.Statements (2) ALONE is sufficient,but (1) ALONE is not sufficient. c. Both statement TOGETHER are sufficient but statement alone is sufficient .Car X traveled from city A to city B in 30 minutes.What was the average speed of car X? (1) Half the distance of the trip was covered at 50 miles per hour, and the other half of the distance was covered at 60 miles per hour.(2) Car X traveled 30 miles during the trip.

Each of the following problem has a question and two statements which are labeled 1. and. Use the data given in 1. and 2. to decide whether the statements are sufficient to answer the question.Select one of the following . a.Statements (1) ALONE is sufficient,but (2) ALONE is not sufficient. b.Statements (2) ALONE is sufficient,but (1) ALONE is not sufficient. c. Both statement TOGETHER are sufficient but statement alone is sufficient . What is the volume of rectangular box S? (1) The total surface of S is 22.(2) The rectangular box S is a cube

Each of the following problem has a question and two statements which are labeled 1. and. Use the data given in 1. and 2. to decide whether the statements are sufficient to answer the question.Select one of the following . a.Statements (1) ALONE is sufficient,but (2) ALONE is not sufficient. b.Statements (2) ALONE is sufficient,but (1) ALONE is not sufficient. c. Both statement TOGETHER are sufficient but statement alone is sufficient . A worker is hired for six days.He is paid Tk.2 more for each day of work than he was paid for the preceding day of work.How much was he paid for the day of work?

Each of the following problem has a question and two statements which are labeled 1. and. Use the data given in 1. and 2. to decide whether the statements are sufficient to answer the question.Select one of the following . a.Statements (1) ALONE is sufficient,but (2) ALONE is not sufficient. b.Statements (2) ALONE is sufficient,but (1) ALONE is not sufficient. c. Both statement TOGETHER are sufficient but statement alone is sufficient . Is K a multiple of 6? (1)K is a multiple of 3. (2) K is a multiple of 12.

A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$  = Angular velocity of precession of the axis of spin)

A rigid body is rotating about an axis. One force F1 acts on the body such that its vector passes through the axis of rotation. Another force F2 acts on it such that it is perpendicular to the axis of rotation and at a point 5cm from the axis. This force F2 is perpendicular to the radius vector at its point of application. Find the net torque on the body. Let F1 = 10N & F2= 5N.