BITSAT2024PhysicsMechanical Properties of SolidsActual
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
Options
- A3 w^2 L 4 R^2 Y
- B3 w^2 L 8 R^2 Y
- C5 w^2 L 8 R^2 Y
- Dw^2 L R^2 Y
Correct answer
C. 5 w^2 L 8 R^2 Y
Step-by-step solution
aligned & l₁= w L (4 R^2 ) Y , l₂= w L R^2 Y & U= 1 2 K₁ ( l₁ )^2+ 1 2 K₂ ( l₂ )^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