The mass of an aluminium rod varies directly with its length. If a 16 cm long rod has a mass of 192 g, find the length of the rod whose mass is 105 g.

Find the thermal resistance of an aluminium rod of length 20cm and area of cross section 1cm^(2) . The heat current is along the length of the rod. Thermal conductivity of aluminium =200Wm^(-1)K^(-1) .

If the linear density of a rod of length L varies as lambda = A+Bx , find the position of its centre of mass .

Three uniform thin rods, each of length L=24 cm, form an inverted U. The vertical rods each have a mass of 14 g, the horizontal rod has a mass of 42 g. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass?

Figure shows a thin uniform rod 50 cm long and has a mass of 100 g . A hollow metal ball is filled with air and has a diameter 10 cm and total mass 50 g is fixed to one end of the rod. At what point along its length will the ball and rod balance horizontally?

Calculate the moment of inertia of a thin rod of mass m and length l about a symmetry axis through the centre of mass and perpendicular to the length of the rod, as shown in Fig.

A uniform rod of length lambda lies on a smooth horizontal table A particle moving on the table has a mass m and a speed v before the collision and it sticks to the rod after the collision. The rod has a mass M then find out. The velocity of the centre of mass C and the angular velocity of the system about the centre of mass after the collision.

An aluminium rod and a copper rod are taken such that their lengths are same and their resistances are also same. The specific resistance of copper is half that of aluminium, but its density is three timesthat of aluminium. The ratio of the mass of aluminium rod and that of copper rod will be :-

A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the centre and stops after the collision. Find a. the velocity of the cente of the rod and b. the angular velocity of the rod abut its centre just after the collision.

Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has same mass. Length of the rod is R, where R is the radius of earth.