JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A solid sphere with uniform density and radius R is rotating initially with constant angular velocity \(\left(\omega_1\right)\) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become \(R / 2\) is \(x \omega_1\). The value of \(x\) is ________
- A 34
- B 30
- C 32
- D 36
Answer & Solution
Correct Answer
(C) 32
Step-by-step Solution
Detailed explanation
When sphere is of radius \(R\), its mass is \(M\), when radius is reduced to \(\frac{\mathrm{R}}{2}\), mass will reduced to \(\frac{\mathrm{M}}{8}\) Now by conservation of angular momentum…
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 radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be \(....m\) Given, the length of the rod is \(10 \sqrt{3} m\).JEE Mains 2022 Medium
- Two capacitors having capacitance \(C _{1}\) and \(C _{2}\) respectively are connected as shown in figure. Initially, capacitor \(C _{1}\) is charged to a potential difference \(V\) volt by a battery. The battery is then removed and the charged capacitor \(C_{1}\) is now connected to uncharged capacitor \(C _{2}\) by closing the switch \(S\). The amount of charge on the capacitor \(C _{2}\), after equilibrium is
JEE Mains 2022 Medium - Let \(\vec A\, = \,(\hat i\, + \,\hat j)\,\) and \(\vec B\, = \,(2\hat i\, - \,\hat j)\,.\) The magnitude of a coplanar vector \(\vec C\) such that \(\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B\) is given byJEE Mains 2018 Hard
- The internal energy of air in \(4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}\) sized room at 1 atmospheric pressure will be _______ \(\times 10^6 \mathrm{~J}\). (Consider air as diatomic molecule)JEE Mains 2025 Easy
- The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy: (Assume \(m_p=m_e \times 1849\) )JEE Mains 2023 Medium
- Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a, b\) and \(c (a < b < c)\) have surface charge densities \(+\sigma,-\sigma\) and \(+\sigma\) respectively. The potential of shell \(B\) isJEE Mains 2018 Hard
More PYQs from JEE Mains
- Let the foci of a hyperbola \(\mathrm{H}\) coincide with the foci of the ellipse \(E: \frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1\) and the eccentricity of the hyperbola \(\mathrm{H}\) be the reciprocal of the eccentricity of the ellipse \(E\). If the length of the transverse axis of \(\mathrm{H}\) is \(\alpha\) and the length of its conjugate axis is \(\beta\), then \(3 \alpha^2+2 \beta^2\) is equal to :JEE Mains 2024 Hard
- If \(2 x^y+3 y^x=20\), then \(\frac{d y}{d x}\) at \((2,2)\) is equal toJEE Mains 2023 Hard
- If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :JEE Mains 2025 Medium
- In the following logic circuit the sequence of the inputs \({A}, {B}\) are \((0,0),(0,1),(1,0)\) and \((1,1)\). The output \(Y\) for this sequence will be :
JEE Mains 2021 Medium - If \(1, \log _{10}\left(4^{x}-2\right)\) and \(\log _{10}\left(4^{x}+\frac{18}{5}\right)\) are in
arithmetic progression for a real number \(x\) then the value of the determinant \(\left|\begin{array}{ccc}2\left(x-\frac{1}{2}\right) & x-1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0\end{array}\right|\) is equal to ...... .JEE Mains 2021 Hard - In an examination, there are \(5\) multiple choice questions with \(3\) choices, out of which exactly one is correct There are \(3\) marks for each correct answer, \(-2\) marks for each wrong answer and \(0\) mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets \(5\) marks is. . . . . ... . .JEE Mains 2022 Hard