dimensions
class 11 HOLIDAY H.W
Q1 Check the correctness of the following relations:
a) V =Pr4/8nl, where Vis the volume per unit time,Pis the pressure,r is the radius,n is the coefficient of viscosity and l is the length.
b) h = 2T cosθ/rdg where h is the height of the liquid ,T is the surface tension of the liquid, ris the radius ,d is the density of the liquid, and g is acceleration due to gravity.
c) The frequency n of a vibrating string of length l under tension F is given by n = 1/2l (F/m)1/2
Where m is the mass per unit length.Check whether this relation is correct or not.
Q 2) Assuming that the volume of a liquid flowing per second (V) through a cylindrical tube depends upon (1) the pressure gradient (p/l) (2) the radius of the tube and (3) the coefficient of viscosity η, find by method of dimensions how it depends on these quantities.
Q 3) The orbital velocity v of a satellite may depend upon its mass , the distance r from the center of the earth and acceleration due to gravity g. By the method of dimensional analysis obtain a relation for the velocity.
Q 4) A body of mass m is moving in a circle of radius r with angular velocity w . Find the expression for the centripetal force f acting on it using method of dimensions
Q5) The value of acceleration due to gravity is 980 cm/s2. What will be its value if the unit of length in kilometer and that of time in minute ?
Q 6) If the unit of force , velocity and energy are 100 dyne , 10 cm/s and 400 erg respectively. What will be unit of mass , length and time?
Q 7) Find the value of 20 joule in a system which has 10 cm, 1 kg and ½ minute as fundamental units of length , mass , and time.
Q8) The radius of a solid sphere is measured to be 11.24 cm. What is the surface area of the sphere to approximate significant figures?
Q 9) The length , breadth and thickness of a block of metal are measured with the help of a metre rod. The results after calculating the errors are
Length = (15.12+_ 0.01 ) cm
Breadth = (10.15 +_ 0.001)cm
Thickness = (5.28+_ 0.01)cm
Find the percentage error in the volume of block.
Q 10)State the no of significant figures in the following:
(1) 0.005 m2 2)2.63 * 10 28 3)0.2560 gcm-3