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1.1 Estimate the energy required for an adult man to walk up through stairs from ground floor to 1st floor?
1.2 Derive formula for the time period of simple pendulum using dimensional analysis.
1.3 If voltage measured across a conductor is 𝑽±∆𝑽=(𝟕.𝟑±𝟎.𝟏) volts and current is𝑰±∆𝑰=(𝟐.𝟕𝟑±𝟎.𝟎𝟓)A. Find the resistance and uncertainty in it.
1.4 If radius of a circular disc is measured as 𝟐.𝟐𝟓𝒄𝒎 with uncertainty ±𝟎.𝟎𝟏𝒄𝒎. Find its surface area with uncertainty in it.
1.1 Estimate that how many floating-point operations can a supercomputer do in 1 day?
1.2 Which of following relationships is dimensionally consistent with an expression yielding a value for acceleration? In these equations, 𝒙 is a distance, 𝒕 is time, and 𝒗 is velocity.
(a) 𝒗/𝒕^𝟐 (b) 𝒗/𝒙^𝟐 (c) 𝒗^𝟐/𝒕 (d) 𝒗^𝟐/𝒙
1.3 The radius of a circle is measured to be (𝟏𝟎.𝟓±𝟎.𝟐)𝒎. Calculate (a) the area and (b) the circumference of the circle, also give the uncertainty in each value.
Q. Encircle the correct option.
Dimension of universal gravitational constant is
(a) [M^(-2) L^3 T^(-2)] (b) [M^3 L^(-1) T^(-2)] (c) [M^(-1) L^3 T^(-2)] (d) [M^(-3) L^3 T^(-2)]
A measurement which on repetition gives same or nearly same result is called
(a) accurate (b) average (c) precise (d) estimated
A student is measuring the time of event by using stopwatch. He takes 5 measurements as: 3.0s, 3.2s, 3.4s, 2.8s, 3.1s. What is the uncertainty in the results?
(a) ±0.3s (b) ±0.6s (c) ±3.1s (d) ±7.75s
Which quantity has different dimension?
(a) Force (b) weight (c) modulus of elasticity (d) Tension
If the dimension of physical quantity are given by [L^a M^b T^c], then the physical quantity will be
(a) force, if a=-1, b=0, c=-2 (b) Pressure, if a=-1, b=1, c=-2
(c) velocity, if a=1, b=0, c=1 (c) acceleration, if a=1, b=1, c=-2
Order of magnitude of (〖10〗^6+〖10〗^3) is
(a) 〖10〗^18 (b) 〖10〗^9 (c) 〖10〗^6 (d) 〖10〗^3
Which of the following may be used as a valid formula to calculate speed of ocean waves?
[v=speed,g=acceleration due to gravity,λ=wavelength,ρ=density,h=depth].
(a) v=√λg (b) v=ρgh (c) gh/λ (d) none
Create a table to show reasonable estimate of some physical quantities.
Express the units of the following derived quantities in terms of base units. (a) Force (b) Work (c) Power (d) Pressure (e) Electric charge
Why is it important to use an instrument of smallest resolution?
What is the importance of increasing the number of readings in an experiment?
What is the difference between precision and accuracy?
What is the principle of homogeneity of dimensions?
A ball is thrown in the air and 5 different students are individually measuring the time it takes to fall back down using stopwatches. The times obtained by each student are the following: 6.2s, 6.0s, 6.4s, 6.1s, 5.8s. (i) What is the uncertainty of the results?
(ii) How should the resulting time be expressed?
The energy of a photon is given by E=hf, find the dimensions of Plank’s constant h, where f is frequency.
Define and explain the term uncertainty.
Discus the rules for calculating uncertainty propagation in the final results in different cases.
What does the dimension of a physical quantity mean? What are its advantages, explain with the help of examples?
What is meant by Estimation of a Physical Quantity? Explain with the help of example.
Estimate number of heartbeats in a lifetime?
Determine the dimensions of each of the following quantities.
a) v^2/ax
b) (at^2)/2
If A=X^2/(Y^2 Z) then find the percentage uncertainty in A. The percentage uncertainty in X, Y and Z are 1%, 1% and 2% respectively.
A spherical ball of radius r experience a resistive force F due to the air as it moves through the air at speed v. The resistive force F is given by the expression F=crv. Where C is constant. By using dimensions, derive the SI base unit of the constant c.
The pressure (P) at a depth (h) in an incompressible fluid of density (ρ) is given by P=ρgh. Where g is the acceleration due to gravity. Check the homogeneity of this equation.
Estimate that how many protons are there in a bacterium?
Estimate that how many hydrogen atoms does it take to stretch across the diameter of the Sun?
The current passing through a resistor R=(13±0.5)Ω is I=(3±0.1)A.
a) Calculate the power consumed (correct to one significant figure).
b) Find the percentage uncertainty of the current passing through the resistor.
c) Find the percentage uncertainty of the resistance.
d) Find the absolute uncertainty of the electrical power.
