iCON Education - Units and Measurements DPT Test

Question 1: Palette 1/12

DPT MCQ

If Gravitational force is given by $F = \frac{G M_1 M_2}{r^2}$, then find the dimensional formula (D.F.) of Gravitational constant $G$.

$[M^{-1}L^3T^{-2}]$

$[ML^3T^{-2}]$

$[M^{-2}L^3T^{-1}]$

$[M^{-1}L^2T^{-2}]$

Question 2: Palette 2/12

DPT MCQ

Find the dimensional formula of the coefficient of viscosity $\eta$, given that the viscous force $F$ is given by $F = 6 \pi \eta r v$, where $r$ is radius and $v$ is velocity.

$[M^1 L^{-1} T^{-1}]$

$[M^1 L^1 T^{-1}]$

$[M^1 L^{-1} T^{-2}]$

$[M^1 L^1 T^{-2}]$

Question 3: Palette 3/12

DPT MCQ

What is the dimensional formula of specific heat capacity ($S$)?

$M^0 L^2 T^{-2} K^{-1}$

$M L^2 T^{-2} K^{-1}$

$M^0 L T^{-2} K^{-1}$

$M^0 L^2 T^{-1} K^{-1}$

Question 4: Palette 4/12

DPT MCQ

Find the dimensional formula of charge if the formula of charge is equal to current $\times$ time.

$[M^0 L^0 T^1 A^1]$

$[M^1 L^0 T^{-1} A^1]$

$[M^0 L^1 T^1 A^{-1}]$

$[M^1 L^1 T^{-2} A^1]$

Question 5: Palette 5/12

DPT MCQ

Find the dimensional formula of electric potential or voltage.

$[M^1 L^2 T^{-2} A^{-1}]$

$[M^1 L^2 T^{-3} A^{-1}]$

$[M^1 L^1 T^{-3} A^{-2}]$

$[M^0 L^2 T^{-3} A^{-1}]$

Question 6: Palette 6/12

DPT MCQ

Find the dimensional formula of resistance.

$[\text{M}^1\text{L}^2\text{T}^{-3}\text{A}^{-1}]$

$[\text{M}^1\text{L}^2\text{T}^{-3}\text{A}^{-2}]$

$[\text{M}^1\text{L}^3\text{T}^{-3}\text{A}^{-2}]$

$[\text{M}^1\text{L}^2\text{T}^{-2}\text{A}^{-2}]$

Question 7: Palette 7/12

DPT MCQ

Find the dimensional formula of resistance.

$[M^1 L^2 T^{-3} A^{-1}]$

$[M^1 L^2 T^{-3} A^{-2}]$

$[M^1 L^3 T^{-3} A^{-2}]$

$[M^1 L^2 T^{-2} A^{-2}]$

Question 8: Palette 8/12

DPT MCQ

If $R = \rho \frac{l}{\text{Area}}$, where $R$ is resistance, $l$ is length, and $\rho$ is resistivity, find the dimensional formula of resistivity.

$[M^1 L^3 T^{-2} A^{-2}]$

$[M^1 L^2 T^{-3} A^{-2}]$

$[M^1 L^3 T^{-3} A^{-2}]$

$[M^1 L^3 T^{-3} A^{-1}]$

Question 9: Palette 9/12

DPT MCQ

Kinetic energy of a particle moving along an elliptical trajectory is given by $K = \alpha s^2$, where $s$ is the distance travelled by the particle. Determine the dimensions of $\alpha$.

$[M^1 L^2 T^{-2}]$

$[M^1 L^1 T^{-2}]$

$[M^0 L^1 T^{-2}]$

$[M^1 L^0 T^{-2}]$

Question 10: Palette 10/12

DPT MCQ

If the centripetal force $F$ acting on a particle depends on its mass $M$, velocity $v$, and radius $r$ as $F = \frac{M v^n}{r}$, find the value of the exponent $n$ using dimensional analysis.

Question 11: Palette 11/12

DPT MCQ

If the formula for the orbital velocity of a satellite is given by $v = \sqrt{\frac{G M}{r^n}}$ where $v$ is orbital velocity, $G$ is the universal gravitational constant, $M$ is the mass of the Earth, and $r$ is the radius of the orbit, find the value of the exponent $n$ for the formula to be dimensionally correct.

Question 12: Palette 12/12

DPT MCQ

If the kinetic energy $KE$ of a body depends on the applied force $F$, velocity $v$, and time $t$ according to the relation $KE = F v^n t$, find the value of the variable exponent $n$ using dimensional analysis.