A particle moves in space along the path $z = ax^3 + by^2$ in such a way that $\frac{dx}{dt} = c = \frac{dy}{dt}.$ Where $a, b$ and $c$ are contants. The acceleration of the particle is
Two particles $A$ and $B$ are moving in $XY$ plane. Particle $A$ moves along a line with equation $y = x$ while $B$ moves along $X$ axis such that their $X$ coordinates are always equal. If $B$ moves with a uniform speed $3\ m/s$ , the speed of $A$ is
The position of a projectile launched from the origin at $t=0$ is given by $\vec{r}=(40 \hat{i}+50 \hat{j}) m$ at $t=$ $2 s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take $g =10\,ms ^{-2}$ )
A horizontal plane supports a stationary vertical cylinder of radius $R = 1\ m$ and a disc $A$ attached to the cylinder by a horizontal thread $AB$ of length $l_0 = 2\ m$ (seen in figure, top view). An intial velocity ($v_0 = 1\ m/s$) is imparted $AB$ to the disc as shown in figure. .......... $\sec$ long will it move along the plane until it strikes against the cylinder ? (All surface are assumed to be smooth)