The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $\mathrm{h}_{\mathrm{m}}$. Here $\mathrm{h}_{\mathrm{m}}$ as function of $\phi$ can be presented as
$$ \text { Match the LIST-I with LIST-II } $$
List - I |
List - II |
||
---|---|---|---|
A. | $$ \text { Gravitational constant } $$ |
I. | $$ \left[\mathrm{LT}^{-2}\right] $$ |
B. | $$ \text { Gravitational potential energy } $$ |
II. | $$ \left[\mathrm{L}^2 \mathrm{~T}^{-2}\right] $$ |
C. | $$ \text { Gravitational potential } $$ |
III. | $$ \left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] $$ |
D. | $$ \text { Acceleration due to gravity } $$ |
IV. | $$ \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] $$ |
Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area $0.5 \mathrm{~m}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the crosssectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is:
$$ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right) $$