System of Parti...

A system consists of 3 particles each of mass m located at points (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are

A man weighing $$60kg$$ is standing on a trolley weighing $$240 kg$$. The trolley is resting on friction less horizontal rails. If the man starts walking on the trolley with a velocity of $$1ms^{-1}$$, then after $$4s$$, his dispalcement relative to the ground is

A body of mass 'm' falls from a height 'h' and rebounds. If 'e' is the coefficient of restitution between the ground and the body, the change in linear momentum of the body is

Figure shows a thin metallic triangular sheet ABC. The mass of the sheet is M. The moment of inertia of the sheet about side AC is : 

Two particles of masses 4 kg and 8 kg are separated by a distance of 12 m. If they are moving toward each other under the influence of a mutual force of attraction, then the two particles will meet each other at a distance of

A scalene triangular lamina of uniform mass density and negligible thickness has one of its vertices at the origin. The position vectors of its other two vertices are $$\vec a$$ and $$\vec b$$. The location of its centre of mass will be  

The moment of inertia of a straight thin rod of mass M and length L about an axis perpendicular to its length and passing through its one end is - 

Two carbon atoms have a non-covalent interaction whose potential energy varies with distance as $$E(r) = 32000000/{r}^{12} 729/{r}^{6},$$ where r is measured in Angstroms. The equilibrium inter-atomic distance will be

A rod of steel is fixed at $$(1,0)$$ and toy is fixed at $$(2,1)$$ on it. The rod is rotated through an angle $$15^{o}$$ in clockwise direction, the new position of the toy will be

The angular velocity of a body changes from $${\omega _1}to\;{\omega _2}$$ without applying torque.The ratio of initial radius of gyration to the final of gyration is-