A wire has mass $(0.3 \pm 0.003)$ gram, radius $(0.5 \pm 0.005)$ mm and length $(6 \pm 0.06)$ cm. The maximum error in the measurement of density is

A batsman hits a ball with a velocity 'v', making an angle of $60^\circ$ with the vertical. After some time direction of velocity is making an angle of $60^\circ$ with the horizontal. The speed of the ball at this instant is
$\left[\cos(60^\circ) = \dfrac{1}{2}, \cos(30^\circ) = \dfrac{\sqrt{3}}{2}\right]$

A particle at rest starts moving with constant angular acceleration '$\alpha$' in a circular path of radius 'r'. At certain instant, the magnitude of centripetal acceleration is $\left(\dfrac{1}{3}\right)^{rd}$ the tangential acceleration. The relation between linear speed (V) and angular acceleration ($\alpha$) is

A car of mass m is crossing the convex bridge of radius of curvature R with speed V. At the highest point the thrust is ($g$ = gravitational acceleration)