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Tutorial Physical Quantities

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PHYSICAL QUANTITIES –TUTORIAL SHEET

1. After being deformed and then let free, a drop of liquid vibrate with a frequency which
appears to depend on the surface tension of drop, the density ρ of the liquid and radius
r of the drop. By means of dimensions, derive an expression for the frequency of
vibration.
2. . (a) Distinguish between a fundamental physical quantity and derived physical quantity?

(b)What is the dimension of physical quantity?

(c) Write the quantities below in dimension form

(i)The coefficient of viscosity

(ii)The surface tension

(iii)The gravitational constant

3. (a) State the uses and limitations of dimensions

(b)Find out whether or not the equation below is dimensionally homogeneous

=k( )

Where k, v, t, p, r, η and L are dimensionless constant, volume, time, pressure, radius,


viscosity constant and length respectively

(c) A wave is produced in taut wire by plucking it, the speed of the wave is said to be
dependent on tension T of the wire, the mass M and length L. Using this information
derive an empirical equation for the speed of the wave in wire.

4. A ball bearing of radius r is released from the surface of the viscous liquid of viscosity
constant η in a tall tube. The bearing attains maximum velocity v as it falls through the
liquid. Given the friction force opposing the motion of the ball as;

F=k

Find numerical value of x, y, and z


5. (a) A student in examination write s = ut + at² as one of the equations of motion he goes
on to check dimensionally its homogeneity and he gets satisfied that he has quoted the
write equation. What is the problem with the formula?

(b)The volume of the fluid flowing through a narrow tube per unit time depends on

pressure gradient , viscosity constant η of the fluid and radius r of the tube. Obtain the
expression for time rate of flow Q.

6. (a) the periodic time T of a simple pendulum is assumed in the form of

T=k

Where k, m, l and g constant, mass of the bob, length of the thread, and acceleration due
to gravity in the same order, Find the numerical values of x, y, and z. Give your comment
on the expression.

(b)A force experienced by an object moving in a circle depends on mass m of the object,
the velocity v at which it moves and radius r of the circle it describes. By using
dimension obtain the expression for the force.

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