Motion In Two Dimensions

A uniform cylinder of mass$M$and radius$R$is to be pulled over a step of height a$\left(a$

A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :

Two particles $A,B$ are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $\omega\,.$ At $t=0,$ their positions and direction of motion are shown in the figure: The relative velocity…

A bead of mass$m$stays at point$P\left(a,b\right)$on a wire bent in the shape of a parabola$y=4Cx^{2}$and rotating with angular speed$\omega\,$(see figure). The value of$\omega\,$is (neglect friction)

A particle of mass $m$is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be :

A projectile is launched at an angle $\alpha\,$with the horizontal with a velocity $20ms^{-1}$. After $10s$, its inclination with horizontal is $\beta\,$. The value of $\tan\,\beta\,$ will be :…

A spring mass system (mass $m,$ spring constant $k$ and natural length $l$) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass…

The position of a projectile launched from the origin at t = 0 is given by $\vec{\text{r}}=\left(40\hat{i}+50\hat{j}\right)\text{m}$ at t = 2s. If the projectile was launched at an angle $\theta\,$from the horizontal,…

The initial speed of a projectile fired from ground is $u$. At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2}u$. The time of flight of the projectile is:

A girl standing on road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}\mathrm{km}h^{-1}$, the rain drops hit her head…

A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v.$If the coefficient of static friction between the tyres and the track is $\mu\,_{s},$then the…

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ},$ the ratio of instantaneous velocity to itsaverage velocity is $\pi\,:x\sqrt{2}.$Thevalue of $x$ will be