Dimensional Analysis

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 say, it is

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

Q. A physcial quantity x depends on quantities y and z as follows: x=Ay+B tan Cz , where A, B and C are constants. Which of the following have different dimensions

1. C and z^-1
2. x and B
3. y and B/A
4. x and A

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

Q.

The heat produced in a wire carrying an eletric current depends on the current, the resistance and the time.

Assuming that the dependence is of the product of powers type, guess an equation between these quantities

using dimensional analysis. The dimensional formula of resistance is $M{L}^2{I}^{-2}{T}^{-3}$and heat is a form of energy.

1. 

2. 

3. 

4. 

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. The period of a body under SHM i.e. presented by T = $P^a{D}^b{S}^c$ ; where P is pressure, D is density and S is surface tension. The value of a, b and c are

1. 
2. 
3. 
4. -1, -2, 3

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. 
2. 
3. 
4. ν² rg

Q.

What is the unit of Density?

1. 

2. 

3. 

4. 

Q. The velocity of a particle depends upon as v = a + bt + $c{t}^2$ ; if the velocity is in m/sec, the unit of a will be

1. m/sec²
2. m²/sec
3. m/sec³
4. m/sec

Q. In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is

1. 0.036
2. 0.36
3. 3.6
4. 36