Physics Chapter on Significant Figures and Dimensions

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Questions and Answers

What is the least count of the watch used in the experiment to measure the time for oscillations?

1 second (correct)

0.1 seconds

0.5 seconds

2 seconds

What is the value of the length L measured in the experiment?

25.0 cm

10.0 cm

15.0 cm

20.0 cm (correct)

What error in the determination of g is indicated in the experiment?

4.4%

2.27%

1.7%

2.7% (correct)

What is the unit of the parameter 'a' in the equation given?

dyne cm4 Signup and view all the answers

Which of the following options represents the dimensions of Reynolds constant?

[ML–1T–1] Signup and view all the answers

What is the formula for velocity as the particle changes with time?

v = t^2 - t Signup and view all the answers

Under what condition can the average speed be zero while the speed is never zero?

When the particle moves in opposite directions with equal distances. Signup and view all the answers

What is the maximum speed a motorcycle can cross a semi-circular bridge of radius 40m without leaving the ground?

20 m/s Signup and view all the answers

What is the relation of static and kinetic friction coefficients between a box and a plank if it slides 4.0 m in 4.0 s?

0.6 and 0.5 Signup and view all the answers

What happens to a rock in an explosion that divides it into three parts?

Two parts go off at right angles to each other. Signup and view all the answers

If two parts of a rock have masses 1 kg and 2 kg with velocities 12 m/s and 8 m/s respectively, what can we infer about their combined motion?

Total energy of the system is conserved. Signup and view all the answers

What does the equation v = t^2 - t indicate about the particle's velocity over time?

The particle experiences changing acceleration. Signup and view all the answers

For a particle moving rectilinearly, what can be concluded about its average velocity and average speed in the same interval?

They can differ based on the path taken. Signup and view all the answers

What is the correct result when multiplying 107.88 by 0.610 expressed with significant figures?

65.81 Signup and view all the answers

Which of the following is classified as a dimensional constant?

Gravitational constant Signup and view all the answers

If E, m, J and G represent energy, mass, angular momentum and gravitational constant respectively, what is the dimensional formula of EJ²/m⁵G²?

length Signup and view all the answers

What is the mean value of the refractive index of water given the values of 1.34, 1.38, 1.32, and 1.36?

1.35 ± 1.48 % Signup and view all the answers

What are the dimensions of the constant related to Io hc?

ML3 T–4 A–2 Signup and view all the answers

What is the fundamental unit ‘u’ formed by combining electric charge ‘e’, Bohr radius ‘a0’, Planck’s constant ‘h’, and speed of light ‘c’ called?

Characteristic unit Signup and view all the answers

To determine the density of a cube, which measurements are primarily used?

Mass and length of its sides Signup and view all the answers

Which option represents the incorrect units of a physics constant?

M–1 L–3 T2 A Signup and view all the answers

Which physical constant has the same units as eV/T?

Boltzmann's constant Signup and view all the answers

What is the dimension of mobility?

M–1T2A Signup and view all the answers

Which mathematical operation is physically meaningful for quantities A and B with different dimensions?

A/B Signup and view all the answers

Which relation correctly expresses the velocity of water waves in terms of wavelength, density, and gravity?

v ∝ gl Signup and view all the answers

From the relation for viscosity in a capillary tube, which expression represents the pressure difference?

p = h(4vl)/(r² - x²) Signup and view all the answers

What is the relation between m and n for the mass of liquid flowing through a tube?

m = –n Signup and view all the answers

What is the correct dimensional formula for AB² if A and B have different dimensions?

Ik²/T Signup and view all the answers

Which option correctly states the dimensions of pressure difference affecting the flow of liquid in a tube?

ML/T² Signup and view all the answers

What is the initial velocity $v_0$ of a particle that bounces back to the same height after losing 50% of its energy in a collision? (Take $g = 10 ms^{-2}$)

20 ms–1 Signup and view all the answers

What is the work done by the cord on a block of mass M raised at a constant downward acceleration of $g/4$ over a distance d?

4Mg Signup and view all the answers

If a body of mass 2 kg has a displacement relation of $x = rac{t^3}{3}$, what is the work done by the body in the first two seconds?

16 joule Signup and view all the answers

During a collision, how much energy does a particle with mass m lose to rebound to the same height?

50% Signup and view all the answers

What is the formula for the force on a particle driven by a machine delivering a constant power k watts at time t?

mk t^{-1/2} Signup and view all the answers

In an elastic collision involving a sphere of mass 8m and a block of mass 2m, which quantity is conserved?

Kinetic Energy Signup and view all the answers

What happens to the height from which a particle rebounds if it loses 50% of its energy in a collision?

Rebounds to a lower height Signup and view all the answers

In the formula $x = rac{t^3}{3}$, what does x represent?

Displacement Signup and view all the answers

Study Notes

Significant Figures and Dimensional Formula

Multiplying 107.88 by 0.610 results in 65.8068, but the answer should be expressed with the correct number of significant figures: 65.81.
The unit 'u' for nanocapacitance is derived from electric charge 'e', Bohr radius 'a0', Planck's constant 'h', and speed of light 'c'.
The dimensional formula of EJ^2/m^5G^2 is the same as that of time, where E represents energy, m represents mass, J represents angular momentum, and G represents the gravitational constant.
The mean value of the refractive index of water with a percentage error is calculated using multiple measurements, resulting in 1.35 ± 1.48%.
The dimensions of eV/T are equivalent to those of Boltzmann's constant, where e is the charge, V is the potential difference, and T is the temperature.

Dimensional Analysis and Physical Relationships

The dimensions of mobility are M^-1T^2A.
Only the mathematical operation of division (A/B) is physically meaningful when A and B have different dimensions.
The velocity of water waves (v) is related to their wavelength (l), the density of water (r), and the acceleration due to gravity (g) by the equation v^2 µ gl.
The dimensional formula for magnetic flux is [ML^2T^-2A^-1].

Work, Energy, and Friction

In the equation P + (a/V^2) = constant, the unit of 'a' is dyne cm^5.
The work done in displacing a body from x = 1 m to x = 5 m can be calculated by analyzing the force-position graph, considering the area under the curve.
The relationship between the force (F) and position (x) of a body is depicted graphically, providing information about the work done during displacement.
The work done by a body in the first two seconds can be calculated by integrating its displacement-time relation.

Kinematics and Dynamics

The time interval for which the particle retards (slows down) is determined by finding the time interval where the velocity (v) is decreasing, given the equation v = t^2 - t.
The greatest speed with which a motorcycle can cross a semicircular bridge without leaving the ground at the highest point is determined by considering the centripetal force and the gravitational force acting on the motorcycle.
The initial velocity of a rock fragment after an explosion can be calculated using the conservation of momentum and the information about the velocities and masses of the other fragments.
The work done by a cord on a block being lowered vertically can be calculated using the formula W = Fd, where F is the force applied by the cord and d is the distance moved.

Power and Motion

The force on a particle at time 't' is proportional to the square root of time, as represented by the equation F = (2mk/t^0.5).
The mass of liquid flowing per second per unit area of cross-section in a tube is proportional to both the pressure difference and the average velocity of the liquid, with a specific relationship between the exponents of these factors.
The Richardson equation I = AT^2e^(-B/kT) describes a relationship between current (I), temperature (T), and other constants.

Viscosity and Gravity

The viscosity of turpentine oil flowing through a capillary tube can be calculated using the Poiseuille's equation, which relates pressure difference, tube length, radius, and velocity to viscosity.
The error in the determination of gravitational acceleration (g) using a simple pendulum can be estimated based on the uncertainties in measuring the length of the pendulum and the time for its oscillations.
The coefficient of static friction and the coefficient of kinetic friction between a box and a plank can be determined based on the angle of inclination at which the box starts to slip and the time taken for it to slide a certain distance.

Forces, Tension, and Motion

The tensions in the cords connecting four blocks of equal mass pulled by a force on a smooth horizontal surface can be calculated using Newton's second law and considering the forces acting on each block.

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Description

This quiz covers significant figures and dimensional analysis in physics, exploring concepts such as the derivation of units and the relationship between physical quantities. Test your understanding of significant figures, dimensional formulas, and physical relationships through practical examples and calculations.