enEnglishguગુજરાતી
JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2013
- Hard
- MCQ
A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(2.08\)
Step-by-step Solution
Detailed explanation
Velocity of the tennis ball on the surface of the earth or ground
\(\begin{array}{l}
v = \sqrt {\frac{{2gh}}{{1 + \frac{{{K^2}}}{{{R^2}}}}}} \,\,(where\,k = radius\,of\,gyration\\
of\,spherical\,shell\, = \sqrt {\frac{2}{3}} R)\\
Horizontal\,range\,AB = \frac{{{v^2}\sin 2\theta }}{g}\\
= \frac{{{{\left( {\sqrt {\frac{{2gh}}{{1 + {k^2}/{R^2}}}} } \right)}^2}\sin \left( {2 \times {{30}^ \circ }} \right)}}{g}
\end{array}\)
More questions from Physics
- A mass of \(50\, {kg}\) is placed at the centre of a uniform spherical shell of mass \(100\, {kg}\) and radius \(50 \,{m}\). If the gravitational potential at a point, \(25\, {m}\) from the centre is \({V} \,{kg} / {m} .\) The value of \({V}\) isJEE Mains 2021 Medium
- The bulk modulus of a liquid is \(3 \times 10^{10}\, Nm ^{-2}\). The pressure required to reduce the volume of liquid by \(2 \%\) is ........ \(\times 10^{8}\; Nm ^{-2}\)JEE Mains 2022 Medium
- In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to .................JEE Mains 2022 Medium
- Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is : (in pF)JEE Mains 2025 Medium
- A copper rod of cross-sectional area \(A\) carries a uniform current \(I\) through it. At temperature \(T\), if the volume charge density of the rod is \(\rho \), how long will the charges take to travel a distance \(d\) ?JEE Mains 2018 Medium
- The elastic limit of brass is \(379\,MPa.\) .......... \(mm\) should be the minimum diameter of a brass rod if it is to support a \(400\,N\) load without exceeding its elastic limit .JEE Mains 2019 Medium
More PYQs from JEE Mains
- Light ray incident along a vector \(\vec{AO}\) \((\vec{AO} = 2\hat{i}-3\hat{j})\) emerges out along vector \(\vec{OB}\) \((\vec{OB} = C\hat{i}-4\hat{j})\) as shown in the figure below. The value of \(C\) is ________.
JEE Mains 2026 Hard - In the experiment of \(Ohm's law,\) a potential difference of \(5.0\, V\) is applied across the end of a conductor of length \(10.0\, cm\) and diameter of \(5.00\, mm .\) The measured current in the conductor is \(2.00\, A\). The maximum permissible percentage error in the resistivity of the conductor isJEE Mains 2021 Hard
- In a series \(L-C-R\) circuit, \(C = 10^{-11}\,Farad.\) \(L = 10^{-5}\,Henry\) and \(R =100\,Ohm.\) when a constant \(D.C.\) voltage \(E\) is applied to the circuit, the capacitor acquires a charge \(10^{-9}\,C\) .The \(D.C.\) source is replaced by a sinusoidal voltage source in which the peak voltage \(E_0\) is equal to the constant \(D.C.\) voltage \(E.\) At resonance the peak value of the charge acquired by the capacitor will beJEE Mains 2013 Hard