Calculate the average life of `79A^(Au^(198))` leaving `t^(1//2)` = 150 days.

Determine the average life of U^(238) having t^(1//2) = 140 days.

The position of an object, moving in one dimension, is given by the formula x (t) = (4.2 t ^(2) + 2.6)m. Calculate its (i) average velocity in the time interval fromj t =0 to t = 3 s and (ii) Instantaneous velocity at t=3s. [ (d (x ^(x)))/( dt ) = nx ^(n -1)]

Calculate the uncertainty in the velocity of a cricket ball of mass 150g , if the uncertainty in its position in of the orer of 1Å . (h=6.6xx10^(-34)kg " "m^(2) s^(-1))

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s^(-1) in a uniform horizontal magnetic field of magnitude 3.0 xx 10^(-2) T. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10 Omega , calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from ?

In hydrogen atom electron makes transist from n = 3 orbit to n = 2 orbit in time 1.2xx10^(-8) s. Then calculate the average torque (in Nm) that acts during this transition.

If a simple pendulum has significant amplitude (up to a factor of (1)/(e) of orginal) only in the period between t = 0 sec to t = tau sec, then tau may be called the average life of pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:

Calculate the decay constant for Ag^(108) if its half life is 2.31 minutes.

The positon of an object moving along x-axis is given by x(t) = (4.2 t ^(2) + 2.6) m, then find the velocity of particle at t =0s and t =3s, then find the average velocity of particle at t =0 s to t =3s.