JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius \(\mathrm{R} / 2\) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
- A \(\frac{7}{32} \mathrm{MR}^2\)
- B \(\frac{9}{32} \mathrm{MR}^2\)
- C \(\frac{17}{32} \mathrm{MR}^2\)
- D \(\frac{13}{32} \mathrm{MR}^2\)
Answer & Solution
Correct Answer
(D) \(\frac{13}{32} \mathrm{MR}^2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & I_{\text {complete }}=\frac{M R^2}{2} \\ & \begin{aligned} I_{\text {removed }} & =\left(\frac{M}{4}\right)\left(\frac{R}{2}\right)^2 \frac{1}{2}+\left(\frac{M}{4}\right)\left(\frac{R}{2}\right)^2 \\ & =\frac{3 M R^2}{32} \\ I=\frac{M R^2}{2} & -\frac{3 M…
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 gas is compressed from a volume of \(2\,m^3\) to a volume of \(1\, m^3\) at a constant pressure of \(100\, N/m^2\). Then it is heated at constant volume by supplying \(150\, J\) of energy. As a result, the internal energy of the gasJEE Mains 2014 Medium
- A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of \(10 \,m\) in \(t \;s ,\) the distance travelled by the toy in the next \(t s\) will be .........\(m\)JEE Mains 2022 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 - A soap bubble of radius \(3\, {cm}\) is formed inside the another soap bubble of radius \(6\, {cm}\). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... \({cm}\)
JEE Mains 2021 Hard - In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness \(t\) and refractive index \(n (=1.5)\), the central fringe shifts by 0.2 cm . The value of t is _________ cm .JEE Mains 2026 Easy
- A particle is projected with velocity \(v_{0}\) along \(x-\) axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e., \(ma =-\alpha x ^{2}.\) The distance at which the particle stops:JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let the circle \(C_1: x^2+y^2-2(x+y)+1=0\) and \(C_2\) be a circle having centre at \((-1,0)\) and radius \(2\) . If the line of the common chord of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) intersects the \(\mathrm{y}\)-axis at the point \(\mathrm{P}\), then the square of the distance of \(\mathrm{P}\) from the centre of \(\mathrm{C}_1\) is :JEE Mains 2024 Hard
- The dimensions of angular momentum , latent heat and capacitance are, respectively.JEE Mains 2013 Hard
- A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to \(60^{\circ}\). The refractive index of the prism material is \(\sqrt{2}\). The angle of incidence (in degrees) is ______.JEE Mains 2025 Easy
- As per given figure, a weightless pulley \(P\) is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if \(g=\) \(10\,m / s ^2\) )
JEE Mains 2023 Medium - A galvanometer having a coil resistance of \(100\ \Omega\). gives a full scale deflection, when a currect of \(I\ mA\) is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of \(10\ A\), is :......\(Ω\)JEE Mains 2016 Medium
- 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