Center of Mass

Assertion: If there are no external forces, the center of mass of a double star moves like a free particle. Reason: If we go to the center of mass frame, then we find that the two stars are moving in a circle about the center of mass, which is at rest.

Four point masses are placede at four corners of a square of side 4m as shown. Match the following columns. {:("Column1","Column2"),("A x-coordinate of center of mass of 4kg and 2kg","P (7//2)m"),("B x-coordinates of center of mass of 4kg 2kg and 3kg","Q (4//3)m"),("C y-coordinate of center of mass of 1kg 4kg and 3kg","R 3m"),("y-coordinate of center of mass of 1kg and 3kg","(20/9)m"):}

Mass Center of a sector of a uniform circular plate Find location of mass center of a sector of a thin uniform plate.

A pulley fixed to the ceiling carries a string with blocks of mass m and 3m attached to its ends. The masses of string and pulley are negligible .When the system is released, its center of mass moves with what acceleration

A circular disc of radius R is removed from a bigger circular disc of radius 2 R such that the circumferences of the discs coincide. The center of mass of new disc is alpha R from the center of the bigger disc. The value of alpha is

Two balls of equal mass are projected from a tower simultaneously with equal speeds. One at angle theta above the horizontal and the other at the same angle theta below the horizontal. The path of the center of mass of the two balls is

Three particles , each of mass m, are placed at the vertices of a right angled triangle as shown in figure. The position vector of the center of mass of the system is (O is the origin and hat(i), hat(j), hat(k) are unit vectors)

A sector cut from a uniform disk of radius 12cm and a uniform rod of the same mass bent into shape of an arc are arranged facing each other as shown in the figure. If center of mass of the combination is at the origin, what is the raius of the arc?

Assertion: When a body dropped from a height explodes in mid air, its center of mass keeps moving in vertically downward directions. Reason: Explosion occurs under internal forces only. External force is zero.

In a two block system in figure match the following. {:("Column1","Column2"),("A Velocity of center of mass","P Keep on changing all the time"),("B Momentum of center of mass","Q First decreases then become zero"),("C Momentum of 1kg block","R Zero"),("D Kinetic energy of 2kg block","S Constant"):}