JEE Mains · Physics · STD 11 - Work,energy,power and collision
- JEE Mains 2025
- Hard
- MCQ
As shown below, bob \(A\) of a pendulum having massless string of length ' \(R\) ' is released from \(60^{\circ}\) to the vertical. It hits another bob \(B\) of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\frac{1}{3} \sqrt{\operatorname{Rg}}\)
Step-by-step Solution
Detailed explanation
Velocity of a just before hitting :
\(\mathrm{u}=\sqrt{2 \mathrm{~g} \frac{\mathrm{R}}{2}}=\sqrt{\mathrm{gR}}\)
Just after collision, let velocity of A and B are \(\mathrm{v}_1\) and \(v_2\) respectively
\(\therefore \text { by COM: }\)
\(\begin{aligned}
& m u=m v_1+\frac{m}{2} v_2 \\
& 2 v_1+v_2=2 u ...(i)\\
& e=1=\frac{v_2-v_1}{u} \\
& \Rightarrow v_2-v_1=u..(ii)
\end{aligned}\)
From (i) -(ii)
\(\Rightarrow 3 \mathrm{v}_1=\mathrm{u} \Rightarrow \mathrm{v}_1=\frac{\mathrm{u}}{3}=\frac{1}{3} \sqrt{\mathrm{gR}}\)
More questions from Physics
- One mole of an ideal monoatomic gas is taken along the path \(ABCA\) as shown in the \(PV\) diagram. The maximum temperature attained by the gas along the path \(BC\) is given by
JEE Mains 2018 Hard - The aperture of the objective is \(24.4\,cm\). The resolving power of this telescope. If a light of wavelength \(2440 \mathring A\) is used to see the object will beJEE Mains 2022 Easy
- A solid cylinder and a solid sphere, having same mass \(M\) and radius \(R\), roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be.JEE Mains 2022 Medium
- In a moving coil galvanometer, two moving coils \(M_1\) and \(M_2\) have the following particulars :
\(\begin{aligned}
& \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\
& \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T}
\end{aligned}\)
Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of \(M_1\) and \(M_2\) ?JEE Mains 2025 Medium - A \(110 \; V , 50 \; Hz , AC\) source is connected in the circuit (as shown in figure). The current through the resistance \(55 \; \Omega\), at resonance in the circuit, will be \(\dots \; A\).
JEE Mains 2022 Medium - A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The rational between temperature and volume for the process is \(TV^x =\) constant, then \(x\) isJEE Mains 2019 Medium
More PYQs from JEE Mains
- The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of increase in density of material, when a pressure \(P\) is applied uniformly on all sides, will beJEE Mains 2021 Medium
- One mole of an ideal diatomic gas expands from volume V to 2 V isothermally at a temperature \(27^{\circ} C\) and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from \(27^{\circ} C\) doing the same amount of work W , then its final temperature will be (close to) ___________ \({ }^{\circ} C\).JEE Mains 2026 Hard