A body of mass m hung at one end of the spring executes SHM. The force constant of spring is K while period of vibration is T. Prove by dimensional method that the equation `T=(2pim)/k`is incorrect.

What is the force constant of a spring which stretched by 0.1m when a mass of 0.5kg is hung from it ?

A body of mass 2 kg performs linear S.H.M. The restoring force acting on it, when its displacement is 0.6 m from the mean position is 3 N. Weite down the differential equation of its motion.

If a spring extends by x on loading, then what is the energy stored by the spring. ( If T is tension in the spring and K is spring constant

Write the Arrhenius equation for the rate constants K_(1) and K_(2) at temperature T_(1) and T_(2) in terms of activation energy E_a .

Show dimensionally that the frequency n of transverse waves in a string of length l and mass per unit length m under a tension T is given by n=K/lsqrt(T/m) .

Mention the factors that affect the rate of chemical reaction. For a reaction, the rate law is k[A]^(1//2)[B] . Can this reaction be an elementary reaction? The rate constant for the first-order decomposition of H_(2)O_(2) is given by the following equation log K =14.2 -(1.0 xx 10^(4)K)/(T) Calculate E_(a) for this reaction and rate constant k if its half life period be 200 min. (R=8.314 JK^(-1)"mol"^(-1))

Check the correctness of the equation by dimensional analysis. n=1/"2l"sqrt(T/m) , n = frequency, m = mass per unit length, T = tension