I couldn't solve these problems. Could you please help me solve them in steps?
Q1. If E,M,J and G respectively denote energy, mass, angular momentum and gravitational constant, Calculate the
dimensions of EJ2 /M5G2
Q2. The frequency of vibration of stretched string depends on its length L its mass per unit length m and the
tension T in the string obtain dimensionally an expression for frequency .
Q3. What is meant by significant figures .State the rules for counting the number of significant figures in a
Q4. A physical quantity X is given by X = A2B3/CD , If the percentage errors of measurement in A,B,C and D
are 4%,2%,3% and 1% respectively, then calculate the % error in X.
Q5. If two resistors of resistance R1=(4 ± 0.5) and R2=(16 ± 0.5) are connected (1) In series and (2) Parallel .
Find the equivalent resistance in each case with limits of % error.
Q6. The length of a rod measured in an experiment was found to be 2.48m, 2.46, 2.50m and 2.48m and 2.49m,
Find the average length , the absolute error in each observation and % error.
Q7. A famous relation in physics relates moving mass m to the rest mass m0 of a particle in terms of its speed v and
the speed of the light c. A boy recalls the relation almost correctly but forgets where to put the constant c. He
m = mo / (1 – v2)1/2
Guess where to put the missing c.
Q8. A calorie is a unit of heat energy and it equals about4.2 J, where 1 J = 4.2 kgm2s-2. Suppose we employ a
system of units in which the unit of mass equals α kg, the unit of length equals β m, the units of time is ϒ sec. show
that a calorie has a magnitude 4.2 α-1 β-2 ϒ2 in terms of the new units.
Q9. In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively, what
are the dimensions of Y in MKS system?
Q10. In an experiment, on the measurement of g using a simple pendulum the time period was measured with an
accuracy of 0.2 % while the length was measured with accuracy of 0.5%. Calculate the percentage error in the
value of g.
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