Three masses m,2 m and 3 m are moving in x−y plane with speed 3u,2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be: 
Held on 12 Apr 2014 · Verified 6 Jul 2026.
12u(i^+3j^)
12u(i^−3j^)
12u(−i^+3j^)
12u(−i^−3j^)
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Net gravitational force at the center of a square is found to be $F_{1}$ when four particles having mass $M, 2 M, 3 M$ and $4 M$ are placed at the four corners of the square as shown in figure and it is $F_{2}$ when the positions of $3 M$ and $4 M$ are interchanged. The ratio $\frac{F_{1}}{F_{2}}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is $\_\_\_\_$. 
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