JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
Two identical solid spheres each of mass \(2\,kg\) and radii \(10\,cm\) are fixed at the ends of a light rod. The separation between the centres of the spheres is \(40\,cm\). The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is \(........... \times 10^{-3}\,kg - m ^2\)
- A \(177\)
- B \(178\)
- C \(198\)
- D \(176\)
Answer & Solution
Correct Answer
(D) \(176\)
Step-by-step Solution
Detailed explanation
\(I =2\left( I _{ cm }+ md ^2\right)\) \(=2\left(\frac{2}{5} mr ^2+ md ^2\right)\) \(=\frac{4}{5} \times 2 \times(0.1)^2+2(2)(0.20)^2\) \(=\frac{8}{5} \times 10^{-2}+16 \times 10^{-2}\) \(=(1.6+16) \times 10^{-2}\) \(=17.6 \times 10^{-2}\) \(I =176 \times 10^{-3}\,kg\,m ^2\)
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 uniform metallic wire is elongated by \(0.04\, m\) when subjected to a linear force \(F\). The elongation, if its length and diameter is doubled and subjected to the same force will be ..... \(cm .\)JEE Mains 2021 Hard
- The moment of inertia of a uniform cylinder of length \(l\) and radius \(R\) about its perpendicular bisector is \(I\). What is the ratio \(l/R\) such that the moment of inertia is minimum?JEE Mains 2017 Hard
- What is the dimensional formula of \(a b^{-1}\) in the equation? \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where letters have their usual meaning.JEE Mains 2024 Hard
- A body of mass 2 kg moving with velocity of \(\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}\) enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of \(\frac{5}{3}\) seconds, then velocity of the body when it emerges from force field isJEE Mains 2025 Easy
- Two short magnetic dipoles \({m}_{1}\) and \({m}_{2}\) each having magnetic moment of \(1\, {Am}^{2}\) are placed at point \({O}\) and \(P\) respectively. The distance between \(OP\) is \(1\, meter.\) The torque experienced by the magnetic dipole \({m}_{2}\) due to the presence of \({m}_{1}\) is ...... \(\times 10^{-7}\, {Nm}\)
JEE Mains 2021 Medium - Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are
JEE Mains 2019 Hard
More PYQs from JEE Mains
- Equation of the line passing through the points of intersection of the parabola \(x^2 = 8y\) and the ellipse \(\frac{{{x^2}}}{3} + {y^2} = 1\) isJEE Mains 2013 Hard
- A bullet of mass \(0.1\, kg\) is fired on a wooden block to pierce through it, but it stops after moving a distance of \(50\, cm\) into it. If the velocity of bullet before hitting the wood is \(10\) \(m / s\) and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is \('x' N.\) The value of \('x'\) to the nearest integer is................. \(N\)JEE Mains 2021 Medium
- At very high frequencies, the effective impendance of the given circuit will be \(....\Omega\)
JEE Mains 2021 Hard - Let \(\left(1+x+2 x^{2}\right)^{20}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{40} x^{40}\) then \(a _{1}+ a _{3}+ a _{5}+\ldots+ a _{37}\) is equal toJEE Mains 2021 Hard
- Let a line passing through the point \((4,1,0)\) intersect the line \(L_1 ; \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) at the point \(\mathrm{A} \quad(\alpha, \beta, \gamma)\) and the line \(L_2: x-6=y=-z+4\) at the point \(B(a, b, c)\).
Then \(\left|\begin{array}{lll}1 & 0 & 1 \\ \alpha & \beta & \gamma \\ \mathrm{a} & \mathrm{b} & \mathrm{c}\end{array}\right|\) is equal toJEE Mains 2025 Hard - Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be.JEE Mains 2022 Medium