UNITS AND DIMENSIONS
UNITS AND MEASUREMENTS
Very short answer type questions
1> Find the area of circle of radius 3.458cm up to correct significant figures.
2> Name the physical quantities whose dimensions are same.
3> State the no. of significant fig. in the following (a)0.007 cm (b)2.64 x 1024kg (c)0.2370 cm
4> Which of the following measurement is more accurate and why? (1)5000.0 cm(2)0.0005cm (3) 6.00cm.
5> Are all dimensionally correct equations numerically correct? Give one example.
6> If x=a+bt+ct2 where x is in meters and t is in second, what is the dimensional formula of ‘a’ , and ‘c’.
7> Write the dimensions formula of (1) Planck’s constant and(2) Rydberg’s constant
Short answer type questions
1>The wavelength ‘λ’ depends mass M of the moving particle its velocity v and planks constant ‘h’ . Show dimensionally the relationship between them.
2>In an experiment the refractive index of the glass was observed to be 1.45, 1.56,1.54,1.44,1.54 and 1.53 . Calculate (1) mean value of the refractive index ;(2) Absolute error ;(3)Fractional error ; (4)Percentage error . Express the result in terms of absolute error and percentage error.
3> If (P+a/V2) (V-b)=RT where the symbols has their usual meanings, then what is the dimension of a/b .
4. If F= a/ b+√d , where f=force ,d= density , then find the dimension of a and b.
5> The factors effecting the time period (T) of the simple pendulum depends on mass , length and acceleration due to gravity . Deduce the relation for time period of the simple pendulum.
6> To determine acceleration due to gravity ,the time of 20 oscillations of a simple pendulum of length 100 cm was observed to be 40 s . calculate the value of ‘g’ and maximum percentage error in the measured value of ‘g’ .
7> If power P=a-x2/b where x represents displacement find the dimension of a and b.
8> A physical quantity Qis given by Q= . A.B3/2/C4D1/2 percentage error in A,B,C,D are 1%, 2%,4%,2% respectively . Find the percentage error in Q.
9>The measured value of length , breadth and height of a block is given as l=12.08+-0.01 cm , b=10.12+-0.01cm . h=5.62+-0.01 cm . Calculate the percentage error in the volume of the block.
10>(a) convert 10 J into ergs . (b) convert 10 N into dyne .
11> A planet moves around the sun , the period of revolution ‘T’ depends upon radius of the orbit ‘R’, mass of the sun ‘M’ and gravitational constant ‘G’, show that T2αR3 .
12>If the length and time period of an oscillating pendulum have errors of 1% and 2% respectively , what is the error in the estimate of ‘g’.