Dimensional Analysis

Q.

In an experiment, the readings for the time period of a simple pendulum are 2.63s, 2.56s, 2.42s, 2.71s and 2.80s.Calculate the relative error and the percentage error?

Q.

The coefficient of thermal conductivity depends upon?

Q.

A unitless quantity

1. never has a nonzero dimension

2. always has a nonzero dimension

3. may have a nonzero dimension

4. does not exist

Q. A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J = 1 kg m2 s¯². Suppose we employ a system of units in which the unit of mass equals a kg, the unit of length equals b m, the unit of time is g s. Show that a calorie has a magnitude 4.2 a ¯¹1 b ¯² g² in terms of the new units.

Q.

When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude a is

1. a/4

2. a/3

3. a/2

4. 2a/3

Q. Note : In stating numerical answers, take care of significant figures. Fill in the blanks (a) The volume of a cube of side 1 cm is equal to .....m³ (b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ...(mm)² (c) A vehicle moving with a speed of 18 km h¯¹ covers....m in 1 s (d) The relative density of lead is 11.3. Its density is ....g cm¯³ or ....kg m¯³.

Q.

The period of oscillation of a simple pendulum of constant length at earth surface is T. Its period inside a mine is

1. Greater than T

2. Less than T

3. Equal to T

4. Cannot be compared

Q.

The displacement of a particle moving in S.H.M. at any instant is given by y = a sin $\omega t$ . The acceleration after time $t=\frac{T}{4}$ is (where T is the time period) [MP PET 1984]

1. aω

2. -aω

3. aω²

4. -aω²

Q. Mass and volume of a block are measured as {22.42g and 4.7cm^3. The maximum possible error in density is

Q.

If there is a positivie error of 50% in the measurement of velocity of a body, find the error in the measurement of kinetic energy, given $△$m = 0.

1. 

2. 

3. 

4. None of these

Q.

The physical quantity impulse has the same dimensions as that of

1. Force

2. Power

3. Energy

4. Momentum

Q. The density of water is 1000kgm^3.the density of water vapor at 100 degree celcius and 1 atm pressure is 0.6 kg per meter cube.the volume of a molecule multiplied by total number gives , what is called molecular volume.estimate the ratio of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure

Q. the thermal capacities of two bodies are in the ratio of 1:4. If the rate of loss of heat are equal for the two bodies under identical conditions of surroundings, then the ratio of rate of fall of temperature of the two bodies is- (1) 1:4 (2) 4:1 (3) 1:8 (4) 8:1

Q. A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ mo of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). boy recalls the relation almost correctly but forgets where to put the constant c. He writes : m = mₒ / (1 - υ ²) ⅟² Guess where to put the missing c.

Q. Fill in the blanks by suitable conversion of units (a) 1 kg m² s¯² = ....g cm² s¯² (b) 1 m = ..... ly (c) 3.0 m s¯² = .... km h¯² (d) G = 6.67 × 10¯¹¹ N m²(kg)¯²= .... (cm)3 s¯² g¯¹

Q. The Poissons ratio of a material is 0.5 .If a force is applied to a wire of this material , there is a decrease in cross sectional area by 4%.The percentage increase in length is

Q.

The dimensional formula of propagation vector $\left(K\right)$ is

1. $\left[M^{0}L{T}^{-1}\right]$

2. $\left[M^0{L}^{-1}{T}^0\right]$

3. $\left[M^1{L}^{-1}{T}^0\right]$

4. $\left[M^{-1}{L}^{-1}{T}^0\right]$

Q. If $u_1$ and $u_2$ are the units selected in two systems of unit of any physical quantity and $n_1$ and $n_2$ are their numerical values then

1. $n_1{u}_1=n_2{u}_2$
2. $n_1+u_1=n_2+u_2$
3. $n_1{n}_2=u_1{u}_2$
4. $n_1{u}_1+n_2{u}_2=0$

Q. 74.When a bob is suspended by light string and it is imparted a horizontal velocity to complete the full circular trajectory in vertical plane. What is the difference in tension between lowest and highest point

Q.

A solenoid $600mm$ long has $50$ turns on it and is wound on an iron rod of $7.5mm$ radius. Find the flux through the solenoid when the current in it, is $3A$. The relative permeability of iron is $600$.

1. $1.66Wb$

2. $1.66nWb$

3. $1.66mWb$

4. $1.66\mu Wb$

5. $1.66pWb$

Q. The measure of mass and volume of a body are 2.00 g and 5.0 cm3 respectively, with possibleerrors of 0.01 g and 0.1 cm3. What would be the maximum permissible error in its density?

Q.

A solenoid of $1.5m$ long with an inner diameter of $4cm$ has three layers of winding of $1000$ turns each & carries a current of $2A$. The magnetic flux through a cross-section of the solenoid is nearly

1. $2.5x{10}^{-7}wb$

2. $6.31x{10}^{-6}wb$

3. $2.1x{10}^{-6}wb$

4. $4.1x{10}^{-5}wb$

Q. The dimensions of the velocity and acceleration are same.

1. False
2. True

Q. The time period of a body in $SHM$ is represented by $T_o=P^a{\rho }^b{S}^c$, where $P$ is pressure, $\rho$ is density and $S$ is surface tension. The value of $a,b$ and $c$ respectively for the relation to be dimensionally correct is

1. $-\frac{3}{2},\frac{1}{2},1$
2. $-1,-2,3$
3. $\frac{1}{2},-\frac{3}{2},-\frac{1}{2}$
4. $1,2,\frac{1}{3}$

Q. If the power of a body is given by $P=xv$, where $v$ is the velocity of the body then the dimension of $x$ is

1. $\left[ML{T}^{-2}\right]$
2. $\left[M{L}^2{T}^{-2}\right]$
3. $\left[ML{T}^2\right]$
4. $\left[M^{2}L{T}^2\right]$

Q. how to determine the direction of progression of a wave from its equation? like many eqn are there eg. Sin(kx-wt) , Sin(wt-kx) etc etc

Q. A man walking briskly in rain with speed υ must slant his umbrella forward making an angle θ with the vertical. A student derives the following relation between θ and v : tan q = υ and checks that the relation has a correct limit: as υ→0, θ →0, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct ? If not, guess the correct relation.

Q. 95. The time period of a simple pendulum are 2.63s, 2.56s, 2.42s2.71sand2.80s calculate the relative error and the percentage error

Q.

Find the odd one out:

1. time

2. weight

3. mass

4. pressure

Q. A standing wave having 11 nodes and 10 antinodesis formed between two atoms having a distance of4.0 A between them. The wavelength of thestanding wave is(2) 0.8. A(1) 2.0 A(3) 0.4 A(4) 1.0 A