JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is \(\frac{1}{ x } MR ^2\), where \(R\) is the radius and \(M\) is the mass of semicircular ring. The value of \(x\) will be \(...........\)
- A \(2\)
- B \(1\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
The moment of inertia of semicircular ring about axis passing through centre of ring and perpendicular to plane of ring is \(= MR ^2\) so \(x=1\)
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 mass \(\mathrm{m}\) is suspended from a spring of negligible mass and the system oscillates with a frequency \(f_1\). The frequency of oscillations if a mass \(9 \mathrm{~m}\) is suspended from the same spring is \(f_2\). The value of \(\frac{f_1}{f_{.2}}\) is _______.JEE Mains 2024 Hard
- The initial velocity \(v_{i}\) required to project a body vertically upward from the surface of the earth to reach a height of \(10\, R ,\) where \(R\) is the radius of the earth, may be described in terms of escape velocity \(v_{ e }\) such that \(v_{i}=\sqrt{\frac{x}{y}} \times v_{ e } .\) The value of \(x\) will be ...... .JEE Mains 2021 Hard
- A solid sphere (\(A\)) of mass \(5m\) and a spherical shell (\(B\)) of mass \(m\), both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of \(A\) and \(B\), they start rolling without slipping with an acceleration of \(a_A\) and \(a_B\), respectively. The ratio of \(a_A\) and \(a_B\) is __________.JEE Mains 2026 Hard
- Young's moduli of the material of wires \(A\) and \(B\) are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \(A\) and \(B\) will be in the ratio of [Assume length of wires \(A\) and \(B\) are same]JEE Mains 2023 Medium
- The following bodies, \((1)\) a ring \((2)\) a disc \((3)\) a solid cylinder \((4)\) a solid sphere, of same mass \(m\) and radius \(R\) are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ........... [Mark the body as per their respective numbering given in the question]
JEE Mains 2021 Hard - A current \(i\) is flowing in a straight conductor of length \(L.\) The magnetic induction at a point on its axis at a distance \(\frac {L}{4}\) from its centre will beJEE Mains 2013 Medium
More PYQs from JEE Mains
- Match the thermodynamic processes taking place in a system with the correct conditions. In the table: \(\Delta Q\) is the heat supplied, \(\Delta W\) is the work done and \(\Delta U\) is change in internal energy of the system
Process Condition \((I)\) Adiabatic \((A)\; \Delta W =0\) \((II)\) Isothermal \((B)\; \Delta Q=0\) \((III)\) Isochoric \((C)\; \Delta U \neq 0, \Delta W \neq 0 \Delta Q \neq 0\) \((IV)\) Isobaric \((D)\; \Delta U =0\) JEE Mains 2020 Medium - Let \(\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) and \(\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) If \(8 x^{2}+b x+c=0\) is a quadratic equation whose roots are \(\alpha^{1 / 5}\) and \(\beta^{1 / 5}\), then the value of \(c-b\) is equal to:JEE Mains 2021 Hard
- A homogeneous solid cylindrical roller of radius \(R\) and mass \(M\) is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder isJEE Mains 2019 Hard
- Given sum of the first \(n\) terms of an \(A.P.\) is \(2n + 3n^2.\) Another \(A.P.\) is formed with the same first term and double of the common difference, the sum of \(n\) terms of the new \(A.P.\) isJEE Mains 2013 Hard
- The shortest distance between the lines \(\vec{r}=\left(\dfrac{1}{3}\hat{i}+2\hat{j}+\dfrac{8}{3}\hat{k}\right)+\lambda(2\hat{i}-5\hat{j}+6\hat{k})\) and \(\vec{r}=\left(-\dfrac{2}{3}\hat{i}-\dfrac{1}{3}\hat{k}\right)+\mu(\hat{j}-\hat{k})\), \(\lambda,\mu \in \mathbb{R}\), is:JEE Mains 2026 Medium
- If \(\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=\) \(Ax ^{3}+ Bx ^{2}+ Cx + D ,\) then \(B + C\) is equal toJEE Mains 2020 Hard