Dimensional Analysis

Q. If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x, y and z such that $P^x{Q}^y{C}^z$ is dimensionless, are

1. x=1, y=1, z=-1
2. x=-1, y=1, z=1
3. x=1, y=-1, z=1
4. x=1, y=1, z=1

Q.

If velocity, time and force were chosen as basic quantities, find the dimensions of mass.

1. 

2. 

3. 

4. None of these

Q. Newton-metre is the SI unit of which of the following quantities?

1. Acceleration
2. Power
3. Work
4. Force

Q.

If velocity (V), force(F) and time(t) are taken to be fundamental quantities and K is the dimensionless constant of proportionality, find the dimensional formula for mass.

1. [KVFT]

2. $\left[K{V}^{-2}FT\right]$

3. $\left[K{V}^{-1}FT\right]$

4. $\left[K{V}^{-1}F{T}^2\right]$

Q. From the equation $tan\theta =\frac{rg}{v^2}$, one can obtain the angle of banking $\theta$ for a cyclist taking a curve (the symbols have their usual meanings). Then $\theta$ is:

1. Dimensionally correct only
2. Both dimensionally and numerically correct
3. Neither numerically nor dimensionally correct
4. Numerically correct only

Q.

Give a daily life example of the statement : Two bodies having same quantity of heat may differ in their temperature and the vice versa.

Q. The equation $(P+\frac{a}{v^2})(v-b)=constant$ . If P and V mean pressure and volume respectively, the C.G.S units of a is:

1. Dyne X cm⁵
2. Dyne X cm⁴
3. Dyne / cm³
4. Dyne / cm²

Q.

A farmer moves along the boundary of a square field of side 10 metre in 40 sec. What will be the magnitude of displacement of the farmer at the end of 2 minutes in 20 sec.from his initial position?

Q. If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is

1. c^1/2G^1/2h^1/2
2. c^1/2G^1/2h^-1/2
3. c^1/2G^-1/2h^1/2
4. c^-1/2G^1/2h^1/2

Q. If the units of force, energy and velocity are $10$ N, $100$ J and $5$ m/s then the unit of mass is :

1. 1 kg
2. 2 kg
3. 3 kg
4. 4 kg

Q. What will be the weight of an object on the earth whose mass is $10$ kg? [$g=10m/s^2$]

Q. The electromagnetic waves travel with a velocity

1. equal to velocity of sound.
2. equal to velocity of light.
3. less than velocity of light.
4. None of the above.

Q. The velocity of an object varies with time as $V={At}^2+Bt+C$. Taking the unit of time as $s$ and velocity as ${ms}^{-1}$, the units of A, B, C respectively are :

1. ${ms}^{-3},{ms}^{-2},{ms}^{-1}$
2. ${ms}^{-2},{ms}^{-1},{ms}^{-3}$
3. ${ms}^{-1},{ms}^{-2},{ms}^{-3}$
4. ${ms}^{-1},{ms}^{-1},{ms}^{-1}$

Q. Using mass $\left(M\right)$, length $\left(L\right)$, time $\left(T\right)$ and electric current $\left(A\right)$ as fundamental quantities the dimensions of permittivity will be

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

Q. Newton-metre is the SI unit of which of the following quantities?

1. Acceleration
2. Power
3. Work
4. Force

Q. Young's modulus of a material has the same units as

1. Pressure
2. Compressibility
3. Force
4. Strain

Q. If the time period of a simple pendulum suspended at a place having $g=9.8m{s}^{-2}$ as the acceleration due to gravity is $T$, the effective length of the pendulum, $l$ is given by:

1. $1.8865T^2$
2. $0.2482T^2$
3. $0.4372T^2$
4. $2.3311T^2$

Q. The length of a simple pendulum executing simple harmonic motion is increased by $21\%$.The percentage increase in the time period of the pendulum of increased length is.

1. $11\%$
2. $21\%$
3. $42\%$
4. $10\%$

Q. The time period of two simple pendulam at are in the ratio 2:1.what will be the ratio of their length?

Q. The energy ($E$), angular momentum ($L$) and universal gravitational constant ($G$) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of planks constant ($h$) is :

1. $0$
2. $1$
3. $-1$
4. $\frac{5}{3}$

Q.

A particle of mass m is executing oscillation about origin on x - axis. Its potential energy is $U\left(x\right)=K|X{|}^n$. If

the time period T is function of its mass, amplitude(a) and k; find the value of n for $T\alpha a^{-\frac{1}{2}}$.

___

Q. If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is

1. c^1/2G^1/2h^1/2
2. c^1/2G^1/2h^-1/2
3. c^1/2G^-1/2h^1/2
4. c^-1/2G^1/2h^1/2

Q. The amount of matter in the unit volume of the substance is its:

1. Relative Density
2. Volume
3. Mass
4. Density

Q. An artificial satellite is in circular orbit around the earth. One of the rockets of the satellite is momentarily fired, the direction of firing of rocket is mentioned in Column I and corresponding change(s) are given in Column II. Match the entries of Column I with the entries of Column II.