The diameter of a spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of vernier scale. One main scale division is $1\, {mm}$. The main scale reading is $10\, {mm}$ and $8^{\text {th }}$ division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of $0.04\, {cm}$, then the radius of the bob is $...... \,\times 10^{-2} \,{cm}$
JEE MAIN 2021, Diffcult
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The time dependence of a physical quantity $P$ is given by $ P = P_0 exp^{(-\alpha t^{2})} $ where $\alpha$ is a constant and $t$ is time. The constant $\alpha$View Solution
- 2A screw gauge gives the following reading when used to measure the diameter of a wire.View Solution
Main scale reading : $0\ mm$
Circular scale reading : $52\ divisions$
Given that $1\ mm$ on main scale corresponds to $100$ divisions of the circular scale. The diameter of wire from the above data is:
- 3Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 mm$. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.View Solution
Measurement condition Main scale reading Circular scale reading Two arms of gauge touching each other without wire $0$ division $4$ division Attempt-$1$: With wire $4$ division $20$ division Attempt-$2$: With wire $4$ division $16$ division What are the diameter and cross-sectional area of the wire measured using the screw gauge?
- 4If $a, b, c$ are the percentage errors in the measurement of $A, B$ and $C$, then the percentage error in $ABC$ would be approximatelyView Solution
- 5The velocity of a freely falling body changes as ${g^p}{h^q}$ where g is acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ areView Solution
- 6Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$View Solution
Assertion $A$ : A spherical body of radius $(5 \pm 0.1)$ $mm$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\,\%$.
Reason $R$ : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below on :
- 7if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ isView Solution
- 8View SolutionThe unit of Young’s modulus is
- 9If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as$ [\eta ^x \rho ^yr^z]$ where $\eta ,\rho $ and $r $ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of $x, y$ and $z$ are given byView Solution
- 10The following observations were taken for determining surface tension $T$ of water by capillary method:View Solution
diameter of capillary, $D= 1.25 \times 10^{-2}\; m$
rise of water, $h=1.45 \times 10^{-2}\; m $
Using $g= 9.80 \;m/s^2$ and the simplified relation $T = \frac{{rhg}}{2}\times 10^3 N/m$ , the possible error in surface tension is ........... $\%$