JEE Mains · Physics · STD 11- 8. mechanical properties of solids
The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of increase in density of material, when a pressure \(P\) is applied uniformly on all sides, will be
- A \(\frac{\rho K }{ P }\)
- B \(\frac{\rho P }{ K }\)
- C \(\frac{ K }{\rho P }\)
- D \(\frac{ PK }{\rho}\)
Answer & Solution
Correct Answer
(B) \(\frac{\rho P }{ K }\)
Step-by-step Solution
Detailed explanation
\(\rho=\frac{M}{V}\) \(\frac{ d \rho}{\rho}=-\frac{ dV }{ V }\) \(K=-\frac{ P }{\frac{ d V }{ V }}\) \(-\frac{ d V }{ V }=\frac{ P }{K}\) \(\frac{ d \rho}{\rho}=\frac{ P }{ K } \Rightarrow d \rho=\frac{\rho P }{ K}\)
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
- A bullet of \(10\, {g}\), moving with velocity \(v\), collides head-on with the stationary bob of a pendulum and recoils with velocity \(100 \, {m} / {s}\). The length of the pendulum is \(0.5\, {m}\) and mass of the bob is \(1\, {kg}\). The minimum value of \(v=\) \(....{m} / {s}\) so that the pendulum describes a circle. (Assume the string to be inextensible and \({g}=10\, {m} / {s}^{2}\) )
JEE Mains 2021 Hard - If the time period \(t\) of the oscillation of a drop of liquid of density \(d\), radius \(r\), vibrating under surface tension \(s\) is given by the formula \(t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} \) . It is observed that the time period is directly proportional to \(\sqrt {\frac{d}{s}} \) . The value of \(b\) should therefore beJEE Mains 2013 Hard
- A concave mirror for face viewing has focal length of \(0.4\,m.\) The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is......\(m\)JEE Mains 2019 Medium
- A block of mass \(5\,kg\) starting from rest pulled up on a smooth incline plane making an angle of \(30^{\circ}\) with horizontal with an affective acceleration of \(1\,ms ^{-2}\). The 10.Power delivered by the pulling force at \(t =10\,s\) from the start is \(.....\,W.\) \(\left[\right.\) Use \(\left.g =10\,ms ^{-2}\right]\) (calculate the nearest integer value)JEE Mains 2023 Hard
- In \(SI\, units\), the dimensions of \(\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} \) isJEE Mains 2019 Medium
- During an adiabatic compression, \(830\, J\) of work is done on \(2\, moles\) of a diatomic ideal gas to reduce its volume by \(50\%\). The change in its temperahture is nearly..... \(K\) \((R\, = 8.3\, J\,K^{-1}\, mol^{-1} )\)JEE Mains 2014 Medium
More PYQs from JEE Mains
- What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' \(h\) ' in terms of the angle of incidence ' \(i\) ' and angle of refraction ' \(r\) ', if the glass slab is placed in air medium?JEE Mains 2025 Medium
- A vertical electric field of magnitude \(4.9 \times 10^{5} N / C\) just prevents a water droplet of a mass \(0.1\, g\) from falling. The value of charge on the droplet will be ........ \(\times 10^{-9} \;C\) \(\left(\right.\) Given \(\left.g =9.8 m / s ^{2}\right)\)JEE Mains 2022 Medium
- Let \( C_{r} \) denote the coefficient of \( x^{r} \) in the binomial expansion of \( (1+x)^{n} \),\(n \in N , 0 \leq r \leq n\). If \( P_{n}=C_{0}-C_{1}+\frac{2^{2}}{3}C_{2}-\frac{2^{3}}{4}C_{3}+....+\frac{(-2)^{n}}{n+1}C_{n}, \) then the value of \( \sum_{n=1}^{25}\frac{1}{P_{2n}} \) equals.JEE Mains 2026 Hard
- Let for two distinct values of \(p\) the lines \(y=x+p\) touch the ellipse \(\mathrm{E}: \frac{\mathrm{x}^2}{4^2}+\frac{\mathrm{y}^2}{3^2}=1\) at the points A and B . Let the line \(\mathrm{y}=\mathrm{x}\) intersect E at the points C and \(D\). Then the area of the quadrilateral \(A B C D\) is equal toJEE Mains 2025 Medium
- Let \(Z\) be the set of integers. If \(A\, = \,\{ x\, \in \,Z\,:\,{2^{(x + 2)({x^2} - 5x + 6)}} = 1\} \) and \(B\, = \,\{ x\, \in \,Z\,:\, - 3\, < \,2x\, - 1\, < \,9\} ,\) then the number of subsets of the set \(A \times B\) isJEE Mains 2019 Hard
- The surface tension of soap solution is \(3.5 \times 10^{-2}\,Nm ^{-1}\). The amount of work done required to increase the radius of soap bubble from \(10\,cm\) to \(20\,cm\) is \(.....\times 10^{-4}\,J\)JEE Mains 2023 Medium