JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity \(3\, m / s\) (as shown in figure). Maximum height with respect to the initial position covered by it will be \(...........cm\).
- A \(75\)
- B \(74\)
- C \(73\)
- D \(72\)
Answer & Solution
Correct Answer
(A) \(75\)
Step-by-step Solution
Detailed explanation
At highest point \(KE _{ f }=0\) Initial \(KE =\) Translational \(KE +\) Rotational \(KE\) \(=\frac{1}{2} mv ^2+\frac{1}{2} I \omega^2\) In case of rolling \(v = R \omega\) \(=\frac{1}{2} m v^2+\frac{1}{2} \times \frac{2}{3} m R^2 \times \frac{v^2}{R^2}\) \(=\frac{5}{6} m v^2\)…
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
- From a solid sphere of mass \(M\) and radius \(R\), a spherical portion of radius \(R/2\) is removed, as shown in the figure. Taking gravitational potential \(V = 0\) at \(r = \infty\), the potential at the centre of the cavity thus formed is
( \(G =\) gravitational constant)
JEE Mains 2015 Hard - Two beams, \(A\) and \(B\), of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam \(A\) has maximum intensity ( and beam \(B\) has zero intensity), a rotation of polaroid through \(30 ^o \) makes the two beams appear equally bright. If the initial intensities of the two beams are \(I_A\) and \(I_B\) respectively, then \(\frac{{{I_A}}}{{{I_B}}}\)=JEE Mains 2014 Medium
- A beam of light has two wavelengths of \(4972\,\mathop A\limits^o \) and \(6216\,\mathop A\limits^o \) with a total intensity of \(3 .6 \times 10^{- 3}\,\,Wm^{-2}\) equally distributed among the two wavelengths. The beam falls normally on an area of \(1\,cm^2\) of a clean metallic surface of work function \( 2.3\,eV.\) Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in \(2\,s\) is approximatelyJEE Mains 2014 Hard
- A carbon resistance has a following colour code. What is the value of the resistance?
JEE Mains 2019 Medium - Match the List\(-I\) with List\(-II\)
Choose the correct answer from the options given belowList \(I\) List \(II\) \(A\) Microwaves \(I\) Radio active decay of the nucleus \(B\) Gamma rays \(II\) Rapid acceleration and deceleration of electron in aerials \(C\) Radio waves \(III\) Inner shell electrons \(D\) \(X\)-rays \(IV\) Klystron valve JEE Mains 2023 Medium - When the \(rms\) voltages \(V_L, V_C\) and \(V_R\) are measured respectively across the inductor \(L\), the capacitor \(C\) and the resistor \(R\) in a series \(LCR\) circuit connected to an \(AC\) source, it is found that the ratio \(V_L : V_C : V_R = 1 : 2 : 3\). If the \(rms\) voltage of the \(AC\) sources is \(100\, V\), the \(V_R\) is close to........\(V\)JEE Mains 2014 Hard
More PYQs from JEE Mains
- If the function
\(f(x)=\left\{\begin{array}{l}\frac{2}{x}\left\{\sin \left(k_1+1\right) x+\sin \left(k_2-1\right) x\right\}, \quad x \lt 0 \\ 4, \quad x=0 \\ \frac{2}{x} \log _e\left(\frac{2+k_1 x}{2+k_2 x}\right), \quad x\gt0\end{array}\right.\)
is continuous at \(\mathrm{x}=0\), then \(\mathrm{k}_1^2+\mathrm{k}_2^2\) is equal toJEE Mains 2025 Medium - The integral \(\int_0^\pi \frac{8 x d x}{4 \cos ^2 x+\sin ^2 x}\) is equal toJEE Mains 2025 Medium
- There are \(5\) points \(\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \mathrm{P}_4, \mathrm{P}_5\) on the side \(\mathrm{AB}\), excluding \(\mathrm{A}\) and \(\mathrm{B}\), of a triangle \(\mathrm{ABC}\). Similarly there are \(6\) points \(\mathrm{P}_6, \mathrm{P}_7, \ldots, \mathrm{P}_{11}\) on the side \(\mathrm{BC}\) and \(7\) points \(\mathrm{P}_{12}, \mathrm{P}_{13}, \ldots, \mathrm{P}_{18}\) on the side \(\mathrm{CA}\) of the triangle. The number of triangles, that can be formed using the points \(\mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{18}\) as vertices, is :JEE Mains 2024 Medium
- The arm \(P Q\) of a rectangular conductor is moving from \(x=0\) to \(x=2 b\) outwards and then inwards from \(x=2 b\) to \(x=0\) as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from \(x=0\) to \(x=b\). Identify the graph showing the variation of different quantities with distance.
JEE Mains 2021 Hard - Let the vectors \((2+a+b) \hat{i}+(a+2 b+c) \hat{j}-(b+c) \hat{k}\) \((1+\mathrm{b}) \hat{i}+2 \mathrm{b} \hat{j}-\mathrm{b} \hat{k}\) and \((2+\mathrm{b}) \hat{i}+2 \mathrm{b} \hat{j}+(1-\mathrm{b}) \hat{k}\) \(\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{R}\) be co-planar. Then which of the following is true?JEE Mains 2021 Hard
- A ball is spun with angular acceleration \(\alpha=6 t ^{2}-2 t\) where \(t\) is in second and \(\alpha\) is in \(rads\) \(^{-2}\). At \(t=0\), the ball has angular velocity of \(10\,rads\) \(^{-1}\) and angular position of \(4\,rad\). The most appropriate expression for the angular position of the ball isJEE Mains 2022 Medium