WBJEE · Physics · Center of Mass Momentum and Collision
There are \(n\) elastic balls placed on a smooth horizontal plane. The masses of the balls are \(m, \frac{m}{2}, \frac{m}{2^2}, \ldots . \frac{m}{2^{n-1}}\) respectively. If the first ball hits the second ball with velocity \(\mathrm{v}_0\), then the velocity of the \(\mathrm{n}^{\text {th }}\) ball will be,
- A \(\frac{4}{3} v_0\)
- B \(\left(\frac{4}{3}\right)^n v_0\)
- C \(\left(\frac{4}{3}\right)^{n-1} v_0\)
- D \(v_0\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{4}{3}\right)^{n-1} v_0\)
Step-by-step Solution
Detailed explanation
Hint : 1st Collision \(\mathrm{V}_1=\frac{2 \times \mathrm{m}}{\frac{\mathrm{m}}{2}+\mathrm{m}} \mathrm{V}_0=\frac{4}{3} \mathrm{~V}_0\) 2nd Collision \(V_2=\frac{2 \times \frac{m}{2}}{\frac{m}{2}+\frac{m}{2^2}} \times V_0=\left(\frac{4}{3}\right)^2 V_0\) 3rd Collision…
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 uniform thin rod of length \(L\), mass \(m\) is lying on a smooth horizontal table. A horizontal impulse \(P\) is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse isWBJEE 2021 Medium
- It is difficult to cook rice in an open vessel by boiling it at high altitudes because ofWBJEE 2009 Medium
- A body floats in water with \(40 \%\) of its volume outside water. When the same body floats in an oil, \(60 \%\) of its volume remains outside oil. The relative density of oil isWBJEE 2011 Hard
- Two coherent monochromatic beams of intensities \(I\) and \(4 I\) respectively are superposed. The maximum and minimum intensitien in the reaulting pattern areWBJEE 2014 Easy
- For Fraunhoffer diffraction to occurWBJEE 2016 Easy
- As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle \(30^{\circ}\), with horizontal for \(\mu_{\mathrm{s}}=0.25\), the block will just start to move for the value of F : [Given \(\mathrm{g}=10 \mathrm{~ms}^{-2}\)]
WBJEE 2024 Hard
More PYQs from WBJEE
- Half-life of a radioactive substance is 20 minute. The time between \(20 \%\) and \(80 \%\) decay will be :WBJEE 2010 Medium
- Consider two concentric conducting sphere of radii \(\mathrm{R}\) and \(2 \mathrm{R}\) respectively. The inner sphere is given a charge \(+\mathrm{Q}\). The other sphere is grounded. The potential at \(r=\frac{3 R}{2}\) isWBJEE 2022 Easy
- The area of the figure bounded by the parabola \(x=-2 y^{2}, x=1-3 y^{2}\) isWBJEE 2020 Hard
- A point charge \(+q\) is placed at the centre of a cube of side \(\mathrm{L}\). The electric flux emerging from the cube isWBJEE 2010 Easy
- An electric cell of emf \(E\) is connected across a copper wire of diameter \(d\) and length \(l\). The drift velocity of electrons in the wire is \(v_{d}\). If the length of the wire is changed to \(2 l,\) the new drift velocity of electrons in the copper wire will beWBJEE 2013 Easy
- \(S_{1}\) and \(S_{2}\) are the coherent point sources of light located in the \(x y\) -plane at points (0,0) and \((0,3 \lambda)\) respectively. Here \(\lambda\) is the wavelength of light. At which one of the following points (given as coordinates), the intensity of interference will be maximum?WBJEE 2013 Medium