A body is projected at t = 0 with a velocity 10 ms^–1 at an angle of 60^o with the horizontal. The radius of curvature of its trajectory at t = 1s is R. neglecting air resistance and taking acceleration due to gravity g = 10 ms^–2, the value of R is :

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $$3.5$$ revolutions per second. A coin placed at a distnce of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : (g = 10 m/s²)

A conical pendulum of length 1 m makes an angle $$\theta $$ = 45^o w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be: (Take g = 10 ms⁻² )

Two cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is