BITSAT 2024 Shift 1 Paper

To determine the work done by the lower block on the upper block, follow these steps:Calculate Maximum Possible Acceleration:The maximum acceleration the upper block ( 1 kg ) can experience without sliding off is due to static friction:$a_{\text{max}} = \mu g = 1\,\mathrm{m}/\mathrm{s}^2$where $\mu$ is the coefficient of friction and $g$ is the acceleration due to gravity.Calculate Common Acceleration:The applied force is distributed over the total mass ( 3 kg ) of the system, so the acceleration $a$ is:$a = \;\frac{F}{m_{\;\text{total }\;}} = \;\frac{0.5}{3} = \;\frac{0.5}{3}\,\mathrm{m}/\mathrm{s}^2$Check for Relative Motion:Since $a < a_{\;\text{max }\;}$, the blocks will move together without slipping.Calculate the Force of Friction:The force of friction acting from the lower block to the upper block is:$f = m_{\;\text{upper }\;} \;\; \cdot a = 1 \cdot \;\frac{0.5}{3} = \;\frac{1}{6}\,\text{N}$Calculate the Work Done by Friction:The work done by this friction force over a displacement of 3 meters is:$W = f \times s = \;\frac{1}{6} \times 3 = 0.5\,\text{J}$Thus, the work done by the lower block on the upper block for a displacement of 3 meters is 0.5 J .