Question
In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^{a} L^{b} T^{c}\right]$. If $b=3$, the value of $c$ is $\qquad$
✓
Answer
(4)
Sol. $\frac{\text { modulus of elasticity }}{\text { Torque }}=\frac{\text { Stress }}{\text { strain } \times \text { torque }}$
$
\begin{aligned}
& =\frac{[\text { Force }]}{[\text { Area }] \times[\text { Force } \times \text { length }]} \\
& =\frac{1}{[\text { Area } \times \text { length }]}=\left[\mathrm{L}^{-3}\right]
\end{aligned}
$
Sol. $\frac{\text { modulus of elasticity }}{\text { Torque }}=\frac{\text { Stress }}{\text { strain } \times \text { torque }}$
$
\begin{aligned}
& =\frac{[\text { Force }]}{[\text { Area }] \times[\text { Force } \times \text { length }]} \\
& =\frac{1}{[\text { Area } \times \text { length }]}=\left[\mathrm{L}^{-3}\right]
\end{aligned}
$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A particle moves along a circle of radius $\left( {\frac{{20}}{\pi }} \right)\,m$ with constant tangential acceleration. If the velocity of the particle is $80 \,m/s$ at the end of the second revolution after motion has begin, the tangential acceleration is
→Twelve conducting rods form the riders of a uniform cube of side $'l'.$ If in steady state, $B$ and $H$ ends of the rod are at $100^o C$ and $0^o C$. Find the temperature of the junction $'A'$ ....... $^oC$
→Two resistance of $100 \Omega$ and $200 \Omega$ are connected in series with a battery of $4 V$ and negligible internal resistance. $A$ voltmeter is used to measure voltage across $100 \Omega$ resistance, which gives reading as $1 V$. The resistance of voltmeter must be $........\ \Omega$.
→Four lowest energy levels of $H-$atom are shown in the figure. The number of possible emission lines would be
→The radius of fifth orbit of the $L ^{++}$is $.........\times 10^{-12}\,m$. Take : radius of hydrogen atom $=0.51 \mathring A$
→A short electric dipole has a dipole moment of $16 \times 10^{-9}\, Cm .$ The electric potential due to the dipole at a point at a distance of $0.6\, m$ from the centre of the dipole, situated on a line making an angle of $60^{\circ}$ with the dipole axis is $.........V$
→$\left(\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} Nm ^{2} / C ^{2}\right)$
A man is riding on a cycle with velocity $7.2$ km/hr up a hill having a slope $1$ in $20. $ The total mass of the man and cycle is $100 kg.$ The power of the man is ............ $W$
→At $100 \,K$ and $0.1$ atmospheric pressure, the volume of helium gas is $10 \,litres.$ If volume and pressure are doubled, its temperature will change to ....... $K$
→Current sensitivity of a moving coil galvanometer is $5\,div/mA$ and its voltage sensitivity (angular deflection per unit voltage applied) is $20\,div/V$. The resistance of the galvanometer is ................. $\Omega$
→Two circuit are shown in the figure $(a)$ and $(b).$ At a frequency of $....\,rad/s$ the average power dissipated in one cycle will be same in both the circuits.
→