Intuition for COM

Q. 11.A circular disc of moment of inertia It is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ωi. Another disc of moment of inertia Ib is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed ωf. The energy lost by the initially rotating disc to friction is : 1) (1/2)[Ib2/(It+Ib)] ωi2 2) (1/2)[It2/(It+Ib)] ωi2 3) [(Ib-It)/(It+Ib)] ωi2 4) (1/2)[(Ib-It)/(It+Ib)] ωi2

Q. A pulley (disc) of mass = 2kg and radius =10cm is attached with the block of mass m1= 4kg and m2=6kg with a light and stretchable string . The angular acceleration of the pulley is (assuming no slipping)

Q. Two masses m1 and m2 connected by a light spring of natural length lo is compressed completely and tied by a string. This system while moving with a velocity v alon8g +X-axis pass through the origin at t=0. At this position the string snaps. Position of mass m1 at time t is given by the equation x1(t) =Vot - A(1 - cosω t). Calculate(a) position of the particle m2 as a function of time.(b) lo in terms of A.

Q. (Torque and Angular Momentum) 10, An angular impulse of 20 Nms is applied to a hollow cylinder of mass 2 kg and radius 20 cm. The change in its angular speed is (1) 25 rad/s (3) 250 rad/s (2) 2.5 rad/s (4) 2500 rad/s f mat 1 ka and radius 10 cm

Q. 3. Four identical spheres each of mass m are placed at the corners of squares of side 2 m.Taking the point of intersection of the diagonals as the orgin, then coordinates of centre of mass are

Q. if the value of acceleration due to gravity at a place decreases by 3% then find the change in the height of mercury in a baromete at that place

Q. 41. The area of the acceleration-displacement curve of a body gives 1. Impulse 2. Change in momentum per unit mass 3. Change in KE per unit mass 4. Total change in energy

Q.

There are two objects of masses 1 kg and 2 kg located at (1, 2) and (-1, 3) respectively. The coordinates of the centre of mass are

1. 

2. 

3. 

4. 

Q. 37. Which of the following is true regarding projectile motion A. Horizontal velocity of projectile is constant B. Momentum is constant

Q.

Half of the rectangular plate shown in figure is made of a material of density $p_1$ and the other half of density $p_2$. The length of the plate is $L$. Locate the centre of mass of the plate.

1. 

2. 

3. 

4. 

Q. Obtain the angular momentum of a particle moving with uniform velocity about any point outside its trajectory.

Q. a disc of mass m and radius r is rotating in a horizontal plane with angular velocity Omega and insect of mass m most from the centre to the circumference of the disc the new angular velocity of the disc

Q. The total torque about the centre of gravity zero. explain

Q. If water is flowing in a pipe with speed 2 m/s then its kinetic energy per unit volume is1) 500 J/m3(3) 1500 J/m3(2) 1000 J/m3(4)2000J/m4

Q. Two particles having mass ratio n:1 are interconnected by a light inextensible string that passes over a smooth pulley. If system is released then acceleration of centre of mass of the particle system is?

Q. What is the centre of mass of a uniform semi circular lamina?

Q. A very large number of particles of same mass m are kept in xy plane at points (1, 1) , (2, 2) , (4, 4) , (8, 8) and so on . The total gravitational feild at the origin has the magnitude

Q.

The centre of mass of a body is located

1. outside the system

2. inside the system

3. at the centre of system

4. inside or outside the system

Q. A body of mass 5 kg is pulled by a force \overrightarrow F=(-4^ i + 3^ j )N from rest on a smooth horizontal table in x z plane. the time at which it will attain a speed of 4m/s i

Q. for pure rolling ofround object as shown the velocity of centre of mass i

Q. where does the centre of mass of a uniform triangular lamina lie

Q. A point mass M is connected at circumference of a uniform disc (M, R). The disc is performing pure rolling motion over rough horizontal surface. If at an ins†an t when the mass is at a height R from surface, angular speed of disc is ω = 1 rad/s, then angular momentum of the system about point of contact on ground is (Given M = 1 kg, R = 1 m)

Q. A solid sphere is released with velocity of centre of mass v at t=0 on a horizontal plane.the velocity of CM when it attains pure rolling

Q. Where the centre of mass of Obtuse triangular lamina lies ? Explain with diagram .

Q. A particle held by a string whose other end is attached to a fixed point C move in a circle on a horizontal frictionless surface . If the string is cut the angular momentum about C will be 1)changes direction but not magnitude 2)increases 3)decreases 4)does not change

Q. 19 Height at which magnitude of acceleration due to gravity will be equal to that at a depth R/2 (where R is radius of earth)

Q. Assertion :- The time period of spring mass system is greater at equator then at poles. Reason :- Time period of spring mass system depends on gravity.

Q. The moment of inertia about an axis normal to the plane and passing through the centre of gravity will be maximum for which of the following bodies of the same mass Options: A disc of radius a Wrong A ring of radius a A square of side 2a Should have chosen A square made by four rods of length 2a

Q. 16. What is internal energy of the system?

Q. A mass m moves in a circle on a smoothhorizontal plane with velocity vo at a radius Ro Themass is attached to a string which passes througha smooth hole in the plane as shown.The tension in the string is increased gradually andfinally m moves in a circle of radius The finalvalue of the kinetic energy is \lbrack AIPMT-2015\rbrack2