JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A solid sphere of radius \(4\) cm and mass \(5\) kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of \(1200\) rpm. It is brought to rest in \(10\) s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are _______ and _______ respectively.
- A \(0.128\pi\) Nm, \(100\)
- B \(0.0128\pi\) Nm, \(50\)
- C \(0.128\pi\) Nm, \(50\)
- D \(0.0128\pi\) Nm, \(100\)
Answer & Solution
Correct Answer
(D) \(0.0128\pi\) Nm, \(100\)
Step-by-step Solution
Detailed explanation
Initial angular velocity \(\omega_0 = 1200 \text{ rpm} = \dfrac{1200 \times 2\pi}{60} = 40\pi \text{ rad/s}\) Final angular velocity \(\omega = 0\) Time \(t = 10 \text{ s}\) Angular acceleration…
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
- There is a small source of light at some depth below the surface of water (refractive index \(=\frac{4}{3}\) ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly)...........\(\%\) [Use the fact that surface area of a spherical cap of height \(\mathrm{h}\) and radius of curvature \(\mathrm{r} \text { is } 2 \pi \mathrm{rh}]\)JEE Mains 2020 Hard
- During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{C_p}{C_v}\) for the gas is:JEE Mains 2024 Hard
- In a Young's double slit experiment, the distance between the two identical slits is \(6.1\) times larger than the slit width. Then the number of intensity maxima observed with in the central maximum of the single slit diffraction pattern isJEE Mains 2014 Medium
- For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \(O\) (the centre of mass) and \(O ^{\prime}(\) corner point \()\) is
JEE Mains 2020 Hard - The value of current \(i_{1}\) flowing from \(A\) to \(C\) in the circuit diagram is\(.......A\)
JEE Mains 2020 Medium - If a rubber ball falls from a height \(h\) and rebounds upto the height of \(h / 2\). The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are _______.JEE Mains 2024 Hard
More PYQs from JEE Mains
- Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason (R) : In isothermal process, \(\mathrm{PV}=\) constant, while in adiabatic process \(\mathrm{PV}^\gamma=\) constant. Here \(\gamma\) is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below :JEE Mains 2025 Medium - The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7\) N/m\(^2\). The percentage decrease in the volume is _____. (Bulk modulus of water \(= 2.1 \times 10^9\) N/m\(^2\).)JEE Mains 2026 Easy
- A bi convex lens of focal length \(10\,cm\) is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is \(...........\,D\).JEE Mains 2023 Medium
- Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?JEE Mains 2020 Hard
- Let \(\alpha, \beta, \gamma\) be the real roots of the equation, \(x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R\) and \(a , b \neq 0)\) If the system of equations (in, \(u,v,w\)) given by \(\alpha u+\beta v+\gamma w=0, \beta u+\gamma v+\alpha w=0\) \(\gamma u +\alpha v +\beta w =0\) has non-trivial solution, then the value of \(\frac{a^{2}}{b}\) isJEE Mains 2021 Hard
- Starting with the same initial conditions, an ideal gas expands from volume \(V_{1}\) to \(V_{2}\) in three different ways. The work done by the gas is \(W_{1}\) if the process is purely isothermal. \(W _{2}\). if the process is purely adiabatic and \(W _{3}\) if the process is purely isobaric. Then, choose the coned optionJEE Mains 2022 Medium