Physics

Q. Terminal velocity of Mars rover depends upon
P = gas density of atmosphere of mars
A = frontal area
W = weight of falling object
What may be the possible relation between terminal velocity $v$ and given quantity.

1. $v=\frac{w}{pA}$
2. $v=\sqrt{\frac{pA}{w}}$
3. $v=\sqrt{\frac{p{A}^3}{w}}$
4. $v=\sqrt{\frac{w}{pA}}$

Q. Terminal velocity of Mars rover depends upon
P = gas density of atmosphere of mars
A = frontal area
W = weight of falling object
What may be the possible relation between terminal velocity $v$ and given quantity.

1. $v=\frac{w}{pA}$
2. $v=\sqrt{\frac{p{A}^3}{w}}$
3. $v=\sqrt{\frac{w}{pA}}$
4. $v=\sqrt{\frac{pA}{w}}$

Q. If $x$ and $a$ stand for distance, then for what value of $n$ in the given equation is dimensionally correct? The equation is $\int \frac{dx}{\sqrt{a^2-x^n}}={\sin }^{-1}\frac{x}{a}$

1. $0$
2. $2$
3. $-2$
4. $1$

Q. Match List I with List II and select the correct answer.
$\begin{array}{cc}\text{List I(Physical quantity)}& \text{List II (Dimensions)}\\ \text{A. Force}& {\text{1. T}}^{-1}\\ \text{B. Angular velocity}& {\text{2. MLT}}^{-2}\\ \text{C. Torque}& {\text{3. ML}}^{-1}{\text{T}}^{-2}\\ \text{D. Stress}& {\text{4. ML}}^{-1}{\text{T}}^{-1}\\ & {\text{5. ML}}^2{\text{T}}^{-2}\end{array}$

1. $A\to 5,B\to 4,C\to 3,D\to 1$
2. $A\to 2,B\to 1,C\to 3,D\to 4$
3. $A\to 1,B\to 2,C\to 3,D\to 5$
4. $A\to 2,B\to 1,C\to 5,D\to 3$

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 dimensionless quantity ______.

1. never has a unit

2. always has a unit

3. may have a unit

4. does not exist

Q. Choose the correct statement(s)

1. A dimensionally correct equation must be physically correct.
2. A dimensionally correct equation may be physically correct.
3. An equation whose L.H.S. and R.H.S. has same values in magnitude must be physically correct.
4. An equation is physically correct when it is dimensionally and mathematically correct.

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. $H=k{l}^2{R}^{2}t$

2. $H=k{l}^{2}Rt$

3. $H=kl{R}^{2}t$

4. $H=klR{t}^2$

Q. A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$ . After some time the velocity of the ball attains a constant value known as terminal velocity $v_r$. The terminal velocity depends on $\left(i\right)$ the mass of the ball $m,\left(ii\right)\eta ,\left(iii\right)rand\left(iv\right)$ acceleration due to gravity $g$ . Which of the following relations is dimensionally correct

1. $v_T\propto \frac{mg}{\eta r}$
2. $v_T\propto \frac{\eta r}{mg}$
3. $v_T\propto \eta rmg$
4. $v_T\propto \frac{mgr}{\eta }$

Q. Density of wood is $0.5\text{g/cc}$ in the $CGS$ system of units. The numerical value of density in $MKS$ system of units is

1. $800$
2. $500$
3. $600$
4. $700$