# Q. At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio $\frac{R_B}{R_A}$ of their activities after time t itself decays with time t as $e^{-3t}$ . [f the half-life of A is $m_2$, the half-life of B is :

JEE Main JEE Main 2019

Solution:

## Half life of $A = \ell n^2$ $t_{1/2} = \frac{\ell n2}{\lambda}$ $\lambda_A = 1$ at $t = 0 \; R_A = R_B$ $N_A e^{- \lambda AT} = N_B e^{-\lambda BT}$ $N_A = N_B$ at $t = 0$ at $t = t \; \frac{R_B}{R_A} = \frac{N_0 e^{\lambda_Bt}}{N_0 e^{- \lambda_A t}}$ $e^{-(\lambda_B - \lambda_A)t} = e^{-t}$ $\lambda_B - \lambda_A = 3$ $\lambda_B = 3 + \lambda_A = 4$ $t_{1/2} = \frac{\ell n2}{\lambda_B} = \frac{\ell n 2}{4}$

You must select option to get answer and solution

## 1. The increase in pressure required to decrease the 200 L volume of a liquid by 0.004% (in kPa) is (Bulk modulus of the liquid ==2100 MPa)

Maharashtra CET 2006 Mechanical Properties Of Solids

## 2. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$ . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-

NEET 2017 System Of Particles And Rotational Motion

## 3. To draw maximum current from a combination of cells, how should the cells be grouped?

AFMC 2006 Current Electricity

## 4. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?

AIPMT 1997 Gravitation

AFMC 2010 Atoms

## 6. The diameter of a flywheel is increased by 1%. Increase in its moment of inertia about the central axis is

JIPMER 2015 System Of Particles And Rotational Motion

## 7. The temperature of 100 g of water is to be raised from 24°C to 90°C by adding steam to it. The mass of the steam required for this purpose is

JIPMER 2015 Thermal Properties Of Matter

## 8. The spectrum of an oil flame is an example for ...........

KCET 2010 Dual Nature Of Radiation And Matter

## 9. A body of mass 4 kg is accelerated upon by a constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is

KCET 2008 Laws Of Motion

## 10. Two equal forces are acting at a point with an angle of 60$^{\circ}$ between them. If the resultant force is equal to $40\sqrt{3}$, the magnitude of each force is

KEAM 2008 Laws Of Motion