A bomb explodes at time t =0 in a uniform, isotropic medium of density and releases energy E, generating a spherical blast wave. The radius R of this blast wave varies with time t as :

Step-by-step solution

The energy will propagate in form of spherical blast wave which is longitudinal in nature. Hence velocity of propagate of disturbance v = P Where P= Pressure array r PV = nRT v = RT V array array l Where V= 4 r³ 3 & v= velocity of propagation = d r d t d r d t = R T ( 4 3 r³ ) d r d t = k r^ 3 / 2 k=c o n s t a n t= 3 R T 4 r^ 3 / 2 d r=k d t r^ 3 / 2 d r= k d t r^ 5 / 2 =k t r=(k t)^ 2 / 5 r t^ 2 / 5 array Hence correct answer is (B) Alternate solution R E ^ a P ^ b t ^ c Dimension of R=L array c L ( ML ² ~T ⁻² )^