Ineed with this question.
an object m1 is suspended by two extensible strings, which pass over smooth pulleys, and is attached to objects m2 and mp3. at m1, the strings are at right angles to each other, and make equal angles with the horizontal. if the mass of m2 is 1.0kg, what are masses of particle m1 and m3?

m1 = √2kg , m2 = 1kg , m3 = 1kg

Explanation:

Since the mass m1 can't move, the sum of horizontal and vertical forces must be zero. Since the mass m1 is suspended symmetrically the horizontal forces are equal if mass m2 and m3 are equal.

The tension in each string suspending mass m1 must match the force of gravity pulling on m1. The tension in each string is:

T = m2*g = m3*g = g

The vertical forces pulling m1 up is therefore: 2 * T * cos 45° = √2 * T = √2 * g

This force must match the force of gravity G pulling m1 down. G = m1 * g

Combining both equations: √2 * g = m1 * g

m1 = √2