A stone is tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u.$ The magnitude of the change in its velocity as it reaches a position where the string is horizontal is
$u-\sqrt{u^{2}-2 g l}$
$\sqrt {2gL}$
$\sqrt {{u^2} - gL}$
$\sqrt {2({u^2} - gL)} $
A projectile is thrown into space so as to have maximum horizontal range $R$. Taking the point of projection as origin, the coordinates of the points where the speed of the particle is minimum are-
A particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where $g$ is acceleration due to gravity)
A particle of mass $m$ is projected with a velocity $V$ making an angle of $45^o$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is
A body slides down a frictionless track which ends in a circular loop of diameter $D$, then the minimum height $h$ of the body in term of $D$ so that it may just complete the loop, is
ball is thrown from a point with a speed $‘v_0$’ at an elevation angle of $\theta $ . From the same point and at the same instant, a person starts running with a constant speed $\frac{{'{v_0}'}}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection $\theta $ ?