Faculty of Engineering
Engineering Physics I (BE121) Course
Fall 2012
Sheet (1)
Units and dimensions
1- Check the dimensional consistency of the following equations:
a) x f = xi + v0  t + a0  t 2
where v0, a0, xi, xf are the initial velocity, the acceleration, the initial
displacement, and the final displacement after a time (t), respectively,
b) T  2
L
g
Where
T: Oscillation time of a simple pendulum.
L: the length of the thread.
g: the acceleration due to gravity.
2- Using dimensional analysis state which one of the following expressions
describes the total circumference of the circular faces, the volume and the area of
the curved surface of the shown truncated cone.
i- (r1+r2)(h2+(r1-r2)2)0.5
ii- 2 (r1+r2)
iii- h(r12+r1r2+r22)
3- The gravitational force exerted by a small object of mass (M) on another object of
a mass (m) is given by: F 
GMm
, where r is the distance separating the two
r2
objects, and G is a constant. Find:
i- The dimensions and units of G.
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3
ii- Check the validity of the equation: g   G  R , where g is the
acceleration due to gravity,  is the average density of the earth and R is
the earth radius.
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Faculty of Engineering
Engineering Physics I (BE121) Course
Fall 2012
4- If you know that the kinetic energy of a body depends on its mass and velocity,
use the dimensional analysis to get the equation of the kinetic energy.
5- Assuming that the mass (m) of a stone that could be drifted by the flow of a river
depends on its speed (v), density () and the acceleration due to gravity (g), prove
using dimensional analysis that m α v6.
6- The centripetal force acting on a rotating object attached to the end of a string
depends on the object mass, its speed and the radius of its circular motion. Find an
expression for the centripetal force.
7- Convert from S.I units to C.G.S and F.P.S units:
i- Acceleration a = 5 m/s2
ii- Power P = 1 watt
iii- Work W= 2 N.m
Assignment
1- Which of the following equations are dimensionally correct?
(a) 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑥
(b) 𝑦 = (2 𝑚) cos(𝑘𝑥), where k = 2 m-1
2- (a) Assume the equation 𝑥 = 𝐴𝑡 3 + 𝐵𝑡 describes the motion of a particular
object, with x having the dimension of length and t having the dimension of time.
Determine the dimensions of the constants A and B. (b) Determine the dimensions
of the derivative
𝑑𝑥
= 3𝐴𝑡 2 + 𝐵
𝑑𝑡
3- A pyramid has a height of 481 ft, and its
base covers an area of 13.0 acres. The
volume of a pyramid is given by the
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expression𝑉 = 𝐵ℎ, where B is the area
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of the base and h is the height. Find the
volume of this pyramid in cubic meters.
(1 acre = 43 560 ft2)
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