91Ó°ÊÓ

Statement-1: In a non-uniform circular motion tangential acecleration arises due to change in magnitude of velocity. Statement-2 : In a non-uniform circular motion centripctal acecleation produce duc to change in direction of velocity.

A stone is projected so as to pass two walls of heights \(a\) and \(b\) at distances \(b\) and \(a\), respectively from the point of projection. Show that the angle of projection must be greater than \(\tan ^{-1}(3)\). Find the range.

Statement-1 : Displacement of a particle is always less than or cqual to the distance travel by the particle. Statement- \(2:\) For a particle moving with constant velocity the distance and displacement has equal magnitude.

A ball is projected horizontally from a height of \(100 \mathrm{~m}\) from the ground with a speed of \(20 \mathrm{~m} / \mathrm{s}\). Find: (a) the time taken to reach the ground, (b) the horizontal distance it covers before striking the ground, and (c) the velocity with which it strikes the ground. Take \(g=10 \mathrm{~m} / \mathrm{s}^{2}\).

Statement-1 : Taking air resistance into accont, time of ascent of a particle projected vertically up is greater than the time of its descent. Statement- \(2: \Lambda\) ir resistance favours the acceleration due to gravity while ascending and opposes it while descending.

Statement-1: If there were no gravitational forec, the path of the projected body always be a straight linc. Statement-2: Gravitational force makes the path of projected body always parabolic.

A projectile is launched with a speod of \(10 \mathrm{~m} / \mathrm{s}\) at an angle \(60^{\circ}\) with the horizontal from a sloping surface of inclination \(30^{\circ}\). The range \(R\) is \(\left(\right.\) Take \(\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (a) \(4.9 \mathrm{~m}\) (b) \(13.3 \mathrm{~m}\) (c) \(9.1 \mathrm{~m}\) (d) \(12.6 \mathrm{~m}\)

A body moving with a constant speod describes a circular path whose radius vector is given by \(\vec{r}-15(\cos p t \hat{i}+\sin p t \hat{j}) \mathrm{m}\) where \(p\) is in \(\mathrm{rad} / \mathrm{s}\), and \(t\) is in second. What is its centripetal acecleration at \(\ell=3 \mathrm{~s}\) ? (a) \(\left(45 p^{2}\right) \mathrm{m} / \mathrm{s}^{2}\) (b) \(\left(5 p^{2}\right) \mathrm{m} / \mathrm{s}^{3}\) (c) \((15 p) \mathrm{m} / \mathrm{s}^{2}\) (d) \(\left(15 p^{2}\right) \mathrm{m} / \mathrm{s}^{2}\)