The identical spheres each of mass 2 M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 m each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is 4 2 x , where the…

Question

The identical spheres each of mass 2 M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 m each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is 4 2 x , where the value of x is ________.

Aicharya · Accepted Answer

Position vector r → COM = m 1 r → 1 + m 2 r → 2 + m 3 r → 3 m 1 + m 2 + m 3 r → COM = 2 M × 0 + 2 M × 4 i ^ + 2 M × 4 j ^ 6 M ⇒ r → = 4 3 i ^ + 4 3 j ^ | r → | = 4 3 2 + 4 3 2 = 4 2 3 Therefore, x = 3 .

The identical spheres each of mass 2 M are placed at the corners of a right angled triangle with mutually…

Solution