MHTCET 13 Apr 2026 Shift 1 Paper

Concept:Conservation of linear momentum applies because the body is initially at rest.Explanation:Initial momentum of the stationary body is zero.After the explosion, the two parts move in opposite directions.By conservation of momentum:$$M_{1} V_{1} = M_{2} V_{2}$$This gives:$$\frac{V_{1}}{V_{2}} = \frac{M_{2}}{M_{1}}$$Kinetic energy of a body is:$$K = \frac{1}{2} m v^{2}$$So the ratio of kinetic energies is:$$\frac{K_{1}}{K_{2}} = \frac{\frac{1}{2} M_{1} V_{1}^{2}}{\frac{1}{2} M_{2} V_{2}^{2}}$$Simplifying:$$\frac{K_{1}}{K_{2}} = \frac{M_{1}}{M_{2}} \left(\frac{V_{1}}{V_{2}}\right)^{2}$$Substitute the velocity ratio:$$\frac{K_{1}}{K_{2}} = \frac{M_{1}}{M_{2}} \left(\frac{M_{2}}{M_{1}}\right)^{2}$$Hence:$$\frac{K_{1}}{K_{2}} = \frac{M_{2}}{M_{1}}$$Answer:The ratio of their kinetic energies is $\frac{M_{2}}{M_{1}}$.Therefore, the correct option is Option B.