PRACTICE PROBLEMS
1. If energy is dependent on the quantities of momentum (p), area (A) and
time (t), establish dimensionally a relationship between these quantities.
2. Calculate the length of the arc of a circle of radius 31.0 cm which
subtends an angle of ฯ/6 at the centre.
3. A new system of units is proposed in which unit of mass is ฮฑ kg, unit of
length ฮฒ m and unit of time ฮณ s. How much will 5J measure in this new
system?
4. The volume of a liquid flowing out per second of a pipe of length l and
radius r is given as ๐ = ๐
8
๐๐4
๐๐ where p is the pressure difference between
the two ends of the pipe and ๐ is the coefficient of viscosity of the liquid
having the dimensional formula [M1L-1T-1]. Check whether the equation is
dimensionally correct.
5. In the equation, : E, m, l and G denote energy, mass,
angular momentum and gravitational constant respectively. Show that P
is a dimensionless quantity.
6. The Moon subtends an angle of 1ยฐ 55โ at the base line equal to the
diameter of the Earth. What is the distance of the Moon from the Earth?
(Radius of the Earth is 6.4 ร 106 m)
7. The angle subtended by the moon at a point on the earth is 0031โ. If the
distance of the moon from earth is 3.84x105km, find the diameter of the
moon.
8. The position function of a particle is x(t)=30tโ5t3.
i. Find the velocity when t=2.
ii. Find the acceleration when t=4.
iii. When is the particle stationary?
9. A particle moves in a straight line so that its position x(t) metres at time t
seconds, relative to a fixed position O, is given by x(t)=t(tโ4)2. Find
i. the velocity at time t
ii. the values of t when the particle is instantaneously at rest
iii. the acceleration after four seconds.
10. A man starts walking from a point on a circular field of radius 0.5 km
and 1 hour later he finds himself at the same point where he initially
started. What is the average speed for the whole journey he travelled? What
is the average velocity of this man for the same?
