Two wires of the same material (Young's modulus =Y ) and same length L but radii R and 2 R respectively, are joined end to end and a weight w is suspended from the combination as shown in the figure. The elastic potential energy in the system is
C. 5 w^2 L 8 R^2 Y
aligned & l_1= w L (4 R^2 ) Y , l_2= w L R^2 Y \\ & U= 1 2 K_1 ( l_1 )^2+ 1 2 K_2 ( l_2 )^2 \\ &= 1 2 Y (4 R^2 ) L [ w L 4 R^2 Y ]^2+ 1 2 Y ( R^2 ) L \\ & [ w L R^2 Y ]^2 ( K= Y A L ) \\ &= 5 w^2 L 8 R^2 Y aligned
Related: Physics — Mechanical Properties of Solids · All PYQ Banks