A particle describes a horizontal circle on smooth inner surface of a cone as shown in figure. If the height of the circle above the vertex is 10 cm . The speed of the particle is (g, acceleration due to gravity =10 ~m / s ^2 )

Step-by-step solution

A particle moves in uniform circular motion on the smooth inner surface of a cone. The vertical component of the normal force balances gravity, while the horizontal component provides centripetal force. Resolving the normal force N acting perpendicular to the surface: N = mg vertically, and N = mv^2/R horizontally. Eliminating N gives = v^2/(Rg) . From the cone's geometry, = h/R . Substituting yields: v^2 = Rg h R = gh With h = 0.1 m and g = 10 m/s ^2 , we obtain: v^2 = (10)(0.1) = 1 m ^2/ s ^2 v = 1 m/s Final answ