JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is \(\left(\frac{x}{100}\right) \% .\) If the relative errors in measuring the mass and the diameter are \(6.0 \%\) and \(1.5 \%\) respectively, the value of \(x\) is
- A \(1000\)
- B \(1075\)
- C \(1060\)
- D \(1050\)
Answer & Solution
Correct Answer
(D) \(1050\)
Step-by-step Solution
Detailed explanation
\(\rho=\frac{M}{V}=\frac{M}{\frac{4}{3} \pi\left(\frac{D}{2}\right)^{3}}\) \(\rho=\frac{6}{\pi} M D ^{-3}\) taking log \(\ell n \rho=\ell n \left(\frac{6}{\pi}\right)+\ell n M -3 \ell m D\) Differentiates \(\frac{ d p}{\rho}=0+\frac{ d M }{ M }-3 \frac{ d ( D )}{ D }\) for…
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
- The width of one of the two slits in Young's double slit experiment is d while that of the other slit is \(x \mathrm{~d}\). If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is \(9: 4\) then what is the value of \(x\) ?
(Assume that the field strength varies according to the slit width.)JEE Mains 2025 Hard - Find the equivalent resistance between two ends of the following circuit
JEE Mains 2025 Easy - In the following circuit, the reading of the ammeter will be : (Take Zener breakdown voltage \(=4 \mathrm{~V})\)
JEE Mains 2025 Medium - A cricket player catches a ball of mass \(120 \mathrm{~g}\) moving with \(25 \mathrm{~m} / \mathrm{s}\) speed. If the catching process is completed in \(0.1 \mathrm{~s}\) then the magnitude of force exerted by the ball on the hand of player will be _______ (in SI unit).JEE Mains 2024 Easy
- Modern vacuum pumps can evacuate a vessel down to a pressure of \(4.0 \times {10^{ - 15}}\, atm\) at room temperature \((300\, K)\). Taking \(R = 8.0\, JK^{-1}\, mole^{-1}\) , \(1\, atm = 10^5\, Pa\) and \(N_ {Avogadro} = 6 \times 10^{23}\, mole^{-1}\) , the mean distance between molecules of gas in an evacuated vessel will be of the order ofJEE Mains 2014 Medium
- A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,N/{A^2}} \right)\)JEE Mains 2019 Medium
More PYQs from JEE Mains
- The square of the distance of the point \((-2, -8, 6)\) from the line \(\dfrac{x-1}{1} = \dfrac{y-1}{2} = \dfrac{z}{-1}\) along the line \(\dfrac{x+5}{1} = \dfrac{y+5}{-1} = \dfrac{z}{2}\) is equal to:JEE Mains 2026 Hard
- Visible light of wavelength \(6000 \times 10^{-8}\; \mathrm{cm}\) falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at \(60^{\circ}\) from the central maximum. If the first minimum is produced at \(\theta_{1},\) then \(\theta_{1}\) is close to.....\(^o\)JEE Mains 2020 Medium
- In a triangle \(ABC,\) right angled at the vertex \(A,\) if the position vectors of \(A, B\) and \(C\) are respectively \(3\hat i\, + \hat j\, - \hat k,\,\, - \hat i\, + 3\hat j\, + p\hat k\) and \(5\hat i\, + q\hat j\, - 4\hat k,\,\) then the point \((p, q)\) lies on a lineJEE Mains 2016 Hard
- The diameter of a sphere is measured using a vernier caliper whose \(9\) divisions of main scale are equal to \(10\) divisions of vernier scale. The shortest division on the main scale is equal to \(1 \mathrm{~mm}\). The main scale reading is \(2 \mathrm{~cm}\) and second division of vernier scale coincides with a division on main scale. If mass of the sphere is \(8.635 \mathrm{~g}\), thedensity of the sphere \(1 \mathrm{~s}\) _______.JEE Mains 2024 Hard
- Let \(\lambda, \mu \in R\). If the system of equations \( 3 x+5 y+\lambda z=3 \) \( 7 x+11 y-9 z=2 \) \( 97 x+155 y-189 z=\mu\) has infinitely many solutions, then \(\mu+2 \lambda\) is equal to :JEE Mains 2024 Hard
- Let the solution curve \(y = y ( x )\) of the differential equation \(\quad \frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{\frac{3}{2}}} y=2 x\) \(\exp \frac{x^3-\tan ^{-1} x^3}{\sqrt{(1+x)^6}}\) pass through the origin. Then \(y (1)\) is equal to:JEE Mains 2023 Hard