1.2 Problems
11
Fig. 1.10
1.47 The mass of the earth is 81% the mass of the moon. The distance between the
centres of the earth and the moon is 60 times the radius of earth R = 6400 km.
Find the centre of mass of the earth–moon system.
1.48 The distance between the centre of carbon and oxygen atoms in CO molecule
is 1.13 Å. Locate the centre of mass of the molecule relative to the carbon
atom.
1.49 The ammonia molecule NH 3 is in the form of a pyramid with the three H
atoms at the corners of an equilateral triangle base and the N atom at the apex
of the pyramid. The H–H distance = 1.014 Å and N–H distance = 1.628 Å.
Locate the centre of mass of the NH 3 molecule relative to the N atom.
1.50 A boat of mass 100 kg and length 3 m is at rest in still water. A boy of mass
50 kg walks from the bow to the stern. Find the distance through which the
boat moves.
1.51 At one end of the rod of length L, a body whose mass is twice that of the rod is
attached. If the rod is to move with pure translation, at what fractional length
from the loaded end should it be struck?
1.52 Find the centre of mass of a solid cone of height h.
1.53 Find the centre of mass of a wire in the form of an arc of a circle of radius R
which subtends an angle 2α symmetrically at the centre of curvature.
1.54 Five identical pigeons are flying together northward with speed v 0 . One of
the pigeons is shot dead by a hunter and the other four continue to fly with
the same speed. Find the centre of mass speed of the rest of the pigeons
which continue to fly with the same speed after the dead pigeon has hit the
ground.
1.55 The linear density of a rod of length L is directly proportional to the distance
from one end. Locate the centre of mass from the same end.
11
Fig. 1.10
1.47 The mass of the earth is 81% the mass of the moon. The distance between the
centres of the earth and the moon is 60 times the radius of earth R = 6400 km.
Find the centre of mass of the earth–moon system.
1.48 The distance between the centre of carbon and oxygen atoms in CO molecule
is 1.13 Å. Locate the centre of mass of the molecule relative to the carbon
atom.
1.49 The ammonia molecule NH 3 is in the form of a pyramid with the three H
atoms at the corners of an equilateral triangle base and the N atom at the apex
of the pyramid. The H–H distance = 1.014 Å and N–H distance = 1.628 Å.
Locate the centre of mass of the NH 3 molecule relative to the N atom.
1.50 A boat of mass 100 kg and length 3 m is at rest in still water. A boy of mass
50 kg walks from the bow to the stern. Find the distance through which the
boat moves.
1.51 At one end of the rod of length L, a body whose mass is twice that of the rod is
attached. If the rod is to move with pure translation, at what fractional length
from the loaded end should it be struck?
1.52 Find the centre of mass of a solid cone of height h.
1.53 Find the centre of mass of a wire in the form of an arc of a circle of radius R
which subtends an angle 2α symmetrically at the centre of curvature.
1.54 Five identical pigeons are flying together northward with speed v 0 . One of
the pigeons is shot dead by a hunter and the other four continue to fly with
the same speed. Find the centre of mass speed of the rest of the pigeons
which continue to fly with the same speed after the dead pigeon has hit the
ground.
1.55 The linear density of a rod of length L is directly proportional to the distance
from one end. Locate the centre of mass from the same end.