MHT CET · Physics · Mechanical Properties of Solids
A metal sphere of radius \(1 \mathrm{~m}\) is charged with \(10^{-2} \mathrm{C}\) in air. Its bulk modulus is
\(10^{11} / 4 \pi^{2}\). The volume strain in the sphere is \(\left(\epsilon_{0}=\right.\) pemittivity of free space)
- A \(\frac{10^{-1}}{6 \in_{0}}\)
- B \(\frac{10^{-14}}{8 \epsilon_{0}}\)
- C \(\frac{10^{-15}}{8 \epsilon_{0}}\)
- D \(\frac{10^{-12}}{4 \in_{0}}\)
Answer & Solution
Correct Answer
(C) \(\frac{10^{-15}}{8 \epsilon_{0}}\)
Step-by-step Solution
Detailed explanation
surface charge density
\(\sigma=\frac{q}{4 \pi r^{2}}=\frac{10^{-2}}{4 \pi \times 1}=\frac{10^{-2}}{4 \pi} \mathrm{C} / \mathrm{m}^{2}\)
strain \(=\)
\(\frac{F}{A}=\frac{1}{2} \frac{\sigma^{2}}{\varepsilon_{2}}=\frac{1}{2 \varepsilon_{0}} \times\left(\frac{10^{-2}}{4 \pi}\right)^{2}=\frac{10^{-4}}{32 \pi^{2} \varepsilon_{0}}\)
strain \(=\frac{\text { stress }}{k}=\frac{1}{2} \frac{\sigma^{2}}{\varepsilon_{0} k}\)
where \(k=\frac{10^{11}}{4 \pi^{2}}\)
substituting and calculating we get strain =
\(\frac{10^{-15}}{8 \varepsilon_{0}}\)
\(\sigma=\frac{q}{4 \pi r^{2}}=\frac{10^{-2}}{4 \pi \times 1}=\frac{10^{-2}}{4 \pi} \mathrm{C} / \mathrm{m}^{2}\)
strain \(=\)
\(\frac{F}{A}=\frac{1}{2} \frac{\sigma^{2}}{\varepsilon_{2}}=\frac{1}{2 \varepsilon_{0}} \times\left(\frac{10^{-2}}{4 \pi}\right)^{2}=\frac{10^{-4}}{32 \pi^{2} \varepsilon_{0}}\)
strain \(=\frac{\text { stress }}{k}=\frac{1}{2} \frac{\sigma^{2}}{\varepsilon_{0} k}\)
where \(k=\frac{10^{11}}{4 \pi^{2}}\)
substituting and calculating we get strain =
\(\frac{10^{-15}}{8 \varepsilon_{0}}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic as at temperature ' \(T\) ' K . The piston of cylinder A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise temperature of the gas in A is ' \(\mathrm{dT}_{\mathrm{A}}\) ', then the rise in temperature of the gas in cylinder B is \(\left(\gamma=\frac{\dot{\mathrm{C}}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}\right)\)MHT CET 2024 Hard
- Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio \(4: 3\). If their surface tensions are in the ratio 6:5, the ratio of heights \(\left(\frac{h_1}{h_2}\right)\) of liquids in the two capillary tubes is (Their angle of contacts are same)MHT CET 2025 Medium
- The relation between total magnetic field (B), magnetic intensity (H), permeability of free space \(\left(\mu_{0}\right)\) and susceptibility \((x)\) isMHT CET 2020 Easy
- A parallel beam of monochromatic light of wavelength \(5 \times 10^{-7} \mathrm{~m}\) is incident
normally on a single narrow slit of width \(10^{-3} \mathrm{~mm}\). At what angle of diffraction,
the first minima is observed?MHT CET 2020 Easy - A circular coil carrying current has radius ' \(R\) '. The distance from the centre of the coil on the axis where the magnetic induction will be \(\frac{1}{27}\) th to its value at the centre of the coil isMHT CET 2025 Medium
- A bomb at rest explodes into 3 parts of same mass. The momentum of two parts is and respectivley. The magnitude of momentum of the third part isMHT CET 2018 Medium
More PYQs from MHT CET
- The solution of the differential equation \(\mathrm{e}^{-x}(y+1) \mathrm{d} y+\left(\cos ^2 x-\sin 2 x\right) y \mathrm{~d} x=0\) at \(x=0\), \(y=1\) isMHT CET 2023 Medium
- If â is a unit vector such that \((\bar{x}-\hat{a}) \cdot(\bar{x}+\hat{a})=8\), then \(|\bar{x}|=\)MHT CET 2021 Medium
- A car sounding a horn of frequency \(1000 \mathrm{~Hz}\) passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is \(11: 9\). If the speed of sound is ' \(v\) ', the speed of the car isMHT CET 2023 Medium
- Two batteries of e.m.f 4 V and 8 V with internal resistance \(1 \Omega\) and \(2 \Omega\) respectively are connected in a circuit with a resistance of \(9 \Omega\) as shown in the figure. The current and potential difference between the points ' P ' and ' Q ' is
MHT CET 2025 Medium - In a game, \(3\) coins are tossed. A person is paid ₹ \(7\), if he gets all heads or all tails; and he is supposed to pay ₹ \(3\), if he gets one head or two heads. The amount he can expect to win on an average per game is ₹MHT CET 2023 Medium
- \(\mathrm{A}(1,-3), \mathrm{B}(4,3)\) are two points on the curve \(y=x-\frac{4}{x}\). The points on the curve, the tangents at which are parallel to the chord \(\mathrm{AB}\), areMHT CET 2023 Easy