1
IAT (IISER) 2023
MCQ (Single Correct Answer)
+4
-1

Two fixed point particles, each of charge $+q$, are separated by a distance $2 L$. Another point charge $+q$ of mass $m$ is oscillating about its equilibrium position as indicated in the figure below. The time period of oscillation is given by $T=$ $2 \pi^{3 / 2} \alpha \sqrt{m} / q$. Given that $\epsilon_0$ is the

permittivity of free space, which of the following options is the dimensionally correct expression for $\alpha$ in SI units?

IAT (IISER) 2023 Physics - Units & Measurement and Dimensions Question 1 English
A
$\epsilon_0^{3 / 2} L$
B
$\epsilon_0^{1 / 2} L$
C
$\epsilon_0^{3 / 2} L^{1 / 2}$
D
$\epsilon_0^{1 / 2} L^{3 / 2}$
2
IAT (IISER) 2023
MCQ (Single Correct Answer)
+4
-1
A quantity has been measured to have a value of 0.00230 in some units. How many significant figures does the measured value have?
A
2
B
3
C
4
D
5
3
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
The fundamental constants are given to be permittivity constant $\left(\epsilon_0\right)$, Planck's constant $(h)$, velocity of light $(c)$, Newton's constant $(G)$ and Boltzmann's constant $\left(k_B\right)$. Which of the following quantities constructed out of the above constant has the dimensions of an electric charge?
A
$\sqrt{\frac{h G}{\epsilon_0^3}}$
B
$\sqrt{h c}$
C
$k_B \sqrt{h c}$
D
$\sqrt{\epsilon_0 h c}$
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