In a nuclear fission reaction of an isotope of mass \(M\), three similar daughter nucler of same mass are formed. The speed of a daughter nuclei in terms of mass defect \(\Delta \mathrm{M}\) will be _______.

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(C) \(c \sqrt{\frac{2 \Delta M}{M}}\)

Step-by-step Solution

Detailed explanation

\((\mathrm{X}) \rightarrow(\mathrm{Y})+(\mathrm{Z})+(\mathrm{P})\)

\(\mathrm{M} \quad \mathrm{M} / 3 \mathrm{M} / 3 \mathrm{M} / 3\)

\(\Delta \mathrm{Mc}^2=\frac{1}{2} \frac{\mathrm{M}}{3} \mathrm{~V}^2+\frac{1}{2} \frac{\mathrm{M}}{3} \mathrm{~V}^2+\frac{1}{2} \frac{\mathrm{M}}{3} \mathrm{~V}^2\)

\(\mathrm{~V}=\mathrm{c} \sqrt{\frac{2 \Delta \mathrm{M}}{\mathrm{M}}}\)

Same subject

Two radioactive materials \(A\) and \(B\) have decay constants \(25 \lambda\) and \(16 \lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \(B\) to that of \(A\) will be "\(e\)" after a time \(\frac{1}{a \lambda}\). The value of \(a\) is \(......\)

JEE Mains 2022 Medium
Two metallic wires \(P\) and \(Q\) have same volume and are made up of same material. If their area of cross sections are in the ratio \(4: 1\) and force \(F_1\) is applied to \(\mathrm{P}\), an extension of \(\Delta l\) is produced. The force which is required to produce same extension in \(Q\) is \(\mathrm{F}_2\).The value of \(\frac{\mathrm{F}_1}{\mathrm{~F}_2}\) is _______.

JEE Mains 2024 Hard
A particle is rotating in a circular path and at any instant its motion can be described as \(\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}\). The angular acceleration of the particle after \(10\) seconds is _______ rad/s\(^2\).

JEE Mains 2026 Medium
Two electric dipoles \(A, B\) with respective dipole moments \(\overrightarrow {{d_A}} = - 4\,qa\,\hat i\) and \(\overrightarrow {{d_B}} = 2\,qa\,\hat i\) are placed on the \(x-\) axis with a separation \(R\), as shown in the figure. The distance from \(A\) at which both of them produce the same potential is

JEE Mains 2019 Hard
A helicopter flying horizontally with a speed of \(360 \mathrm{~km} / \mathrm{h}\) at an altitude of 2 km , drops an object at an instant. The object hits the ground at a point O , 20 s after it is dropped. Displacement of ' O ' from the position of helicopter where the object was released is :
(use acceleration due to gravity \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) and neglect air resistance)

JEE Mains 2025 Medium
A water drop of radius \(1\,\mu m\) falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is \(1.8 \times 10^{-5}\,Nsm ^{-2}\) and its density is negligible as compared to that of water \(10^{6}\,gm ^{-3}\). Terminal velocity of the water drop is________ \(\times 10^{-6}\,ms ^{-1}\) (Take acceleration due to gravity \(=10\,ms ^{-2}\) )

JEE Mains 2022 Medium

Explore more questions on app