Q 7.10(b) Given the moment of inertia of a disc of mass and radius about any of its
diameters to be , find its moment of inertia about an axis normal to the
disc and passing through a point on its edge.
Q7.10 (a) Find the moment of inertia of a sphere about a tangent to the sphere, given the
moment of inertia of the sphere about any of its diameters to be , where
is the mass of the sphere and is the radius of the sphere.
Q7.9 A car weighs . The distance between its front and back axles is . Its
centre of gravity is behind the front axle. Determine the force exerted by the
level ground on each front wheel and each back wheel.
Q7.8 A non-uniform bar of weight is suspended at rest by two strings of negligible
weight as shown in Fig.7.39. The angles made by the strings with the vertical are
and respectively. The bar is long. Calculate the distance of the
centre of gravity of the bar from its left end.
Q7.7 Two particles, each of mass and speed , travel in opposite directions along parallel
lines separated by a distance . Show that the angular momentum vector of the two
particle system is the same whatever be the point about which the angular momentum is taken.
Q7.6 Find the components along the axes of the angular momentum of a particle, whose position vector is with components and momentum is with components, and . Show that if the particle moves only in the plane the angular momentum has only a z-component.
Q7.5 Show that is equal in magnitude to the volume of the parallelepiped formed
on the three vectors , , and .
Q7.4 Show that the area of the triangle contained between the vectors is one half
of the magnitude of .
Q7.3 A child sits stationary at one end of a long trolley moving uniformly with a speed V
on a smooth horizontal floor. If the child gets up and runs about on the trolley in any
manner, what is the speed of the CM of the (trolley + child) system?
Q7.2 In the HCl molecule, the separation between the nuclei of the two atoms is about
. Find the approximate location of the CM of the molecule,
given that a chlorine atom is about times as massive as a hydrogen atom and
nearly all the mass of an atom is concentrated in its nucleus.
Q7.1 Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv)
cube, each of uniform mass density. Does the centre of mass of a body necessarily
lie inside the body?