Six forces lying in a plane and forming angles of $60^{0}$ relative to one another are applied to the centre of a homogeneous sphere with a mass m = 6kg. These forces are radially outward and consecutively 1N, 2n, 3N, 4N, 5N and 6N. The acceleration of the sphere is

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Solution

The particle is acted upon by $6$ forces radially outwards. Net force along each diameter is $3 N$ . Thus, three forces of $3 N$ with an angle of $60$ degrees between them are acting on the sphere.

Then resultant will have three force each of $3 N$ at $0, 60, 120 d e g r e e s .$

Then resultant of it will have two force of $3 N$ and $3 \sqrt{3}$ at angle $90$

Then resultant will be $\sqrt{3^{2} + {3 \sqrt{3}}^{2}} = \sqrt{36} = 6$

The resultant of these forces will be 6 N.
Thus acceleration of the particle will be 6/6 = 1 N

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Six forces lying in a plane and forming angles of 600 relative to one another are applied to the centre of a homogeneous sphere with a mass m = 6kg. These forces are radially outward and consecutively 1N, 2n, 3N, 4N, 5N and 6N. The acceleration of the sphere is

Six forces lying in a plane and forming angles of $60^{0}$ relative to one another are applied to the centre of a homogeneous sphere with a mass m = 6kg. These forces are radially outward and consecutively 1N, 2n, 3N, 4N, 5N and 6N. The acceleration of the sphere is