MHTCET 11 Apr 2026 Shift 2 Paper

Concept:In a perfectly inelastic collision, the two masses stick together and move with a common velocity. Linear momentum of the system is conserved because no external force acts during the collision.Explanation:Write the initial momentum of each mass separately along the X-axis and Y-axis.For mass $M$ moving along X-axis with velocity $V\hat{i}$:$$\vec{p}_1 = M(V\hat{i}) = MV\hat{i}$$For mass $2M$ moving along Y-axis with velocity $3V\hat{j}$:$$\vec{p}_2 = 2M(3V\hat{j}) = 6MV\hat{j}$$Total initial momentum of the system:$$\vec{p}_i = MV\hat{i} + 6MV\hat{j}$$After sticking, the total mass becomes:$$M + 2M = 3M$$Let the common velocity after collision be $\vec{v}$. Using conservation of linear momentum:$$3M\vec{v} = MV\hat{i} + 6MV\hat{j}$$Divide both sides by $3M$:$$\vec{v} = \frac{V}{3}\hat{i} + 2V\hat{j}$$Answer:The velocity of the combination after the collision is $\frac{V}{3}\hat{i} + 2V\hat{j}$, which is Option B.