A body of mass 'm' is moving with speed 'V' along a circular path of radius 'r'. Now the speed is reduced to $$\frac{V}{2}$$ and radius is increased to '3r'. For this change, initial centripetal force needs to be

A body attached to one end of a string performs motion along a vertical circle. Its centripetal acceleration, when the string is horizontal, will be [$$\mathrm{g}=$$ acceleration due to gravity]

A projectile is thrown with an initial velocity $$(a \hat{i}+b \hat{j}) \mathrm{m} / \mathrm{s}$$, where $$\hat{i}$$ and $$\hat{j}$$ are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it, then

A particle is performing U.C.M. along the circumference of a circle of diameter $$50 \mathrm{~cm}$$ with frequency $$2 \mathrm{~Hz}$$. The acceleration of the particle in $$\mathrm{m} / \mathrm{s}^2$$ is