JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)
- A \(4\)
- B \(3\)
- C \(5\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
For ring \(I=m R_1^2=m K_1^2\) \(\therefore\) Radius of gyration \(K_1=R_1\) For solid sphere \(I^{\prime}=\frac{2}{5} m^{\prime} R_2^2=m^{\prime} K_2^2\) \(\therefore \text { Its radius of gyration }=K_2=\sqrt{\frac{2}{5}} R_2\) \(\because K_1=K_2\)…
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
- Two charges \(7 \mu C\) and \(-2 \mu C\) are placed at \((-9,0,0) cm\) and \((9,0,0) cm\) respectively in an external field \(E=\frac{ A }{ r ^2} \hat{ r }\), where \(A=9 \times 10^5 N / C . m ^2\).
Considering the potential at infinity is 0 , the electrostatic energy of the configuration is ___________ J .JEE Mains 2026 Medium - Given below are two statements : Statement\(-I:\) Acceleration due to gravity is different at different places on the surface of earth. Statement\(-II:\) Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given belowJEE Mains 2023 Medium
- A \(10\,V\) battery with internal resistance \(1\,\Omega \) and a \(15\,V\) battery with internal resistance \(0.6\,\Omega \) are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to ................ \(V\)
JEE Mains 2015 Hard - If the series limit frequency of the Lyman series is \(v_L\), then the series limit frequency of the \(P\)-fund series isJEE Mains 2018 Medium
- A parallel plate capacitor with plate area \(A\) and plate separation \(d =2 \,m\) has a capacitance of \(4 \,\mu F\). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \(K =3\) (as shown in figure) will be .........\( \mu \,F\)
JEE Mains 2022 Hard - The magnitude of the magnetic field at the centre of an equilateral triangular loop of side \(1\,m\) which is carrying a current of \(10\,A\) is:......\(\mu T\) [Take \(\mu _0 = 4\pi \times 10^{-7}\,NA^{-2}\)]JEE Mains 2019 Medium
More PYQs from JEE Mains
- Let \([ x ]\) denote the greatest integer \(\leq x\). Consider the function \(f(x)=\max \left\{x^2, 1+[x]\right\}\). Then the value of the integral \(\int \limits_0^2 f ( x ) dx\) is :JEE Mains 2023 Hard
- A simple harmonic oscillator has an amplitude \(A\) and time period \(6 \pi\) second. Assuming the oscillation starts from its mean position, the time required by it to travel from \(x=A\) to \(x=\frac{\sqrt{3}}{2} A\) will be \(\frac{\pi}{x}\) s, where \(x=\) _______.JEE Mains 2024 Hard
- A rod of length eight units moves such that its ends \(A\) and \(B\) always lie on the lines \(x-y+2=0\) and \(y+2=0\), respectively. If the locus of the point \(P\), that divides the rod \(A B\) internally in the ratio \(2: 1\) is \(9\left(x^2+\alpha y^2+\beta x y+\gamma x+28 y\right)-76=0\), then \(\alpha-\beta-\gamma\) is equal to :JEE Mains 2025 Hard
- The velocity of a particle executing SHM varies with displacement \(( x )\) as \(4 v ^2=50- x ^2\). The time period of oscillations is \(\frac{x}{7} s\). The value of \(x\) is \(............\) \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\)JEE Mains 2023 Medium
- Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) be a twice differentiable function such that \(f(2)=1\). If \(\mathrm{F}(x)=x f(x)\) for all \(x \in \mathbf{R}\), \(\int_0^2 x \mathrm{~F}^{\prime}(x) \mathrm{d} x=6\) and \(\int_0^2 x^2 \mathrm{~F}^{\prime \prime}(x) \mathrm{d} x=40\), then \(\mathrm{F}^{\prime}(2)+\int_0^2 \mathrm{~F}(x) \mathrm{d} x\) is equal to :JEE Mains 2025 Medium
- A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field \(B =0.8\,T\). When released the radius of the loop starts shrinking at a constant rate of \(2\,cm ^{-1}\). The induced emf in the loop at an instant when the radius of the loop is \(10\,cm\) will be \(........mV\).JEE Mains 2023 Medium