Dimensional Analysis

Q. The position of a particle at time t is given by the relation x(t)= $\left(\frac{v_0}{\alpha }\right)(1-c^{-at})$ where $v_0$ and $\alpha$ are constants . The dimensions of $v_0$ and $\alpha$ are respectively

1. M^oL¹T^-1 and T
2. M^oL¹T^-1 and T^-1
3. M^oL¹T^o and T^-1
4. M^oL¹T^-1 and LT^-2

Q. The unit of $\frac{L}{R}$ is (where L= inductance and R= resistance)

1. sec
2. volt
3. Ampere
4. sec^-1

Q.

Young's modulus of steel is $19\times {10}^{10}\frac{N}{m^2}$. Express it in $\frac{dyne}{c{m}^2}$. Here dyne is the CGS unit of force.

1. 

2. 

3. 

4. None of these

Q.

Identify the pair whose dimensions are equal.

1. Force and work

2. Stress and energy

3. Force and stress

4. Torque and work

Q. ____ is the positive terminal of a dry cell.

1. Metal disc
2. Metal case
3. Metal cap
4. Metal base

Q.

In a direct impact, loss in kinetic energy is given by $△K=\frac{M_1{M}_2}{2(M_1+M_2)}.(V_1-V_2{)}^2(1-K^2)$ with usual

notations(except k). The quality k will have dimensional formula:

1. 

2. 

3. 

4. 

Q.

Two pendula start swinging simultaneously. By the time the first pendulum makes 20 oscillations, $2^{nd}$ pendulum makes 15 oscillations. The ratio of their lengths is:

1. 

2. 

3. 

4. 

Q.

If two different quantities have the same unit then they must have the same dimension.

1. False
2. True

Q.

The SI unit of pressure is ___ .

Q.

The position of a particle at time t is given by the relation $x\left(t\right)=\frac{v_o}{\alpha }(1-c^{-\alpha t})$

$v_o$ and $c$ are constants . The dimensions of $v_o$ and $\alpha$ are respectively:

1. M^oL¹T^-1 and T
2. M^oL¹T^-1 and T^-1
3. M^oL¹T^o and T^-1
4. M^oL¹T^-1 and LT^-2

Q. Which of the following sets alone cannot enter the list of fundamental quantities in any system of units?

(A) Length, mass, and speed
(B) Length, time, and speed
(C) Mass, time, and speed
(D) Length, time, and mass [1 Mark]

Q.

What are the units of relative density?

1. $kg/m^3$

2. $m^3$

3. no units

4. $kg$

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

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

Q. A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius r and length l and having a pressure difference P across its end, is

1. 
2. 
3. 
4. 

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

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

Q. Find odd one out .
Length, mass , time , velocity

Q. If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is

1. cg³p^-2
2. c^-1g^op^-1
3. c²g^op^-2
4. c^og²p^-1

Q. In S = a + bt + $c{t}^2$. S is measured in metres and t in seconds. The unit of c is

1. None
2. m
3. ms^-1
4. ms^-2

Q. The velocity of water waves $v$ may depend upon their wavelength $\lambda$ the density of water $\rho$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as

1. ν² rg
2. 
3. 
4. 

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

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

Q. What is the maximum number of quantities you can imagine the time period of pendulum to depend upon?

1. 3
2. 4
3. 5
4. No idea

Q.

density of aluminium is 2.7 g/cm CUBE express the density in kg/m cube

Q. The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f =C$m^x{K}^y$; where C is a dimensionless quantity. The value of x and y are

1. 
2. 
3. 
4. 

Q. The expression $\left[M{L}^{-1}{T}^{-2}\right]$ does not represent

1. pressure
2. power
3. Young's modulus
4. stress

Q. An objest has a mass of volume 3 cubic metre and density 6000 kilogram per cubic metre .What is its mass?

Q.

CALCULATE THE VOLUME OF WOOD OF MASS 6000KG WHEN THE DENSITY OF WOOD IS 0.8g/m³ .

Q. State the relation between Volume and Density.​

Q.

a piece of wood of mass 150g has a volume of 200cm³ .find the density of wood in (a)CGS system (b) S.I. SYSTEM.

Q.

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

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

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

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