Concepts Of Physics MCQ Edition [Volume 1]PhysicsCircular Motion
A particle is projected with a speed u at an angle to the horizontal. Determine the radius of curvature of the parabola traced by the projectile at the position where the particle velocity makes an angle /2 with the horizontal.
Options
- Au^2 ^2 g ^2( /2)
- Bu^2 ^2 g ^3( /2)
- Cu^2 ^2 g ^3( /2)
- Du^2 ^2 g ^3( /2)
Correct answer
C. u^2 ^2 g ^3( /2)
Step-by-step solution
The horizontal component of velocity remains constant throughout the projectile motion. Let v be the velocity of the particle when it makes an angle /2 with the horizontal. Equating the horizontal components of velocity: v ( /2) = u v = u ( /2) The radius of curvature at any point on the trajectory is given by = v^2 a_n , where a_n is the normal component of acceleration. The only acceleration acting on the projectile is the acceleration due to gravity g , which acts vertically downwards. The component of g perpend