Embibe Experts Solutions for Chapter: Units and Measurement, Exercise 1: Exercise 1

Consider a particle moving along the positive direction of $X$-axis. The velocity of the particle is given by $\mathrm{v}=\alpha \sqrt{x}$ ($\alpha$ is a positive constant). At time $t=0$, if the particle is located at $x=0$, the time dependence of the velocity and the acceleration of the particle are respectively.

A huge circular arc of length $4.4 \mathrm{ly}$ subtends an angle $4\mathrm{s}$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8 \mathrm{AU}$ per second?
Given : $1 \mathrm{ly}=9.46\times {10}^{15} \mathrm{m}$

$1 \mathrm{AU}=1.5\times {10}^{11} \mathrm{m}$

Match the physical quantities with their correct $\mathrm{SI}$ units.

The correct match is

The main scale division and pitch of a screw gauge is $0.05 \mathrm{cm}$. Number of circular scale division in the circular scale is $100$. When no object is placed between the studs then the $0$ of main scale is not visible and $5^{\mathrm{th}}$ division of circular scale coincides with the main scale. When a wire is placed in between the studs then the reading on main scale is $4.6 \mathrm{mm}$ and ${52}^{\mathrm{nd}}$ division on circular scale matches with reference line on main scale. The actual diameter of wire is

In a vernier callipers, the least count of main scale is $1 \mathrm{mm}.$ $20$ division of vernier scale are matching with $19$ divisions of main scale. The thickness of the object measured by the vernier callipers will be :

Which of the following units denotes the dimensions $\frac{M{L}^2}{Q^2}$, where $Q$ denotes the electric charge?

An object falls for a time of $0.25 \mathrm{s}$. The acceleration of free fall is $9.81 \mathrm{m} {\mathrm{s}}^{-2}$. The displacement is calculated. Which of the following gives the correct number of significant digits for the calculated value of the displacement of the object?

How many significant figures should be written in the sum $4.56 \mathrm{g}+9.032 \mathrm{g}+580.0078 \mathrm{g}+540.439 \mathrm{g}$ ?