Find the scalar and vector
products of two vectors. a = (3î-4j+5k)
and b =(-2î+j+3k)
Find the centre of mass of a
uniform L-shaped lamina (a thin flat plate)
with dimensions as shown. The mass of
the lamina is 3 kg.
Find the centre of mass of
three particles at the vertices of an
equilateral triangle. The masses of the
particles are 100g, 150g, and 200g
respectively. Each side of the equilateral
triangle is 0.5m long.
The oxygen molecule has a mass of 5.30 × 10-26 kg and a moment of inertia of
1.94 ×10-46 kg m2
about an axis through its centre perpendicular to the lines joining
the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and
that its kinetic energy of rotation is two thirds of its kinetic energy of translation.
Find the average angular velocity of the molecule.
A metre stick is balanced on a knife edge at its centre. When two coins, each of mass
5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be
balanced at 45.0 cm. What is the mass of the metre stick?
From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The centre
of the hole is at R/2 from the centre of the original disc. Locate the centre of gravity
of the resulting flat body.
To maintain a rotor at a uniform angular speed of 200 rad s-1, an engine needs to
transmit a torque of 180 N m. What is the power required by the engine ?
(Note: uniform angular velocity in the absence of friction implies zero torque. In
practice, applied torque is needed to counter frictional torque). Assume that the
engine is 100% efficient.
A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius
40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a
force of 30 N ? What is the linear acceleration of the rope ? Assume that there is no
slipping.
(a) A child stands at the centre of a turntable with his two arms outstretched. The
turntable is set rotating with an angular speed of 40 rev/min. How much is the
angular speed of the child if he folds his hands back and thereby reduces his
moment of inertia to 2/5 times the initial value ? Assume that the turntable
rotates without friction.
(b) Show that the child’s new kinetic energy of rotation is more than the initial
kinetic energy of rotation. How do you account for this increase in kinetic energy?
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