A vehicles of mass 10 quintals climba up a hill 200m high and thenmoves on a level road with a velocity of \({36}{k}{m}/{h}\) .Calculate its total mechanical energy while running on the top of the hill.
Answer
Here, \({m}={10}\) qunitals\(={1000}{k}{g}.\) \({h}={200}{m}.\) \({v}={36}{k}{m}/{h}=\frac{{{36}\times{1000}}}{{{60}\times{60}}}{m}/{s}={10}{m}/{s}.\) Potential energy gained. \({U}={m}{g}{h}={1000}\times{9.8}\times{200}={1.96}\times{10}^{{{6}}}{J}\) KE of car, \({k}=\frac{{{1}}}{{{2}}}{m}{v}^{{{2}}}=\frac{{{1}}}{{{2}}}\times{1000}{\left({10}\right)}^{{{2}}}\) \(={0.5}\times{10}^{{{5}}}{J}\) Mechanical energy \(={U}+{K}\) \(={1.96}\times{10}^{{{6}}}+{0.5}\times{10}^{{{5}}}={2.01}\times{10}^{{{6}}}{J}\)
A very small particle rests on the top of a hemisphere of radius \({20}{c}{m}\). Calculate the smallest horizontal velocity to be given to it if it is to leave the hemisphere without sliding down its surface, take \({g}={9.8}{m}/{s}^{{{2}}}\).
A cylinder of radius \({R}\) and mass \({M}\) rolls without slipping down a plane inclined at an angle \(\theta\). Coeff. of friction between the cylinder and the plane is \(\mu\). For what maximum inclination \(\theta\), the cylinder rolls without slipping ? (A) \({{\tan}^{{-{1}}}\mu}\) (B) \({{\tan}^{{-{1}}}{\left({3}\mu\right)}}\) (C) \({{\tan}^{{-{1}}}{2}}\mu\) (D) \({{\tan}^{{-{1}}}.}\frac{{{3}}}{{{2}}}\mu\)
What volume of \({3}\) molar \({H}{N}{O}_{{{3}}}\) is needed to oxidise \({8}{g}\) of \({F}{e}^{{{3}+}}\), \({H}{N}{O}_{{{3}}}\) gets converted to \({N}{O}\) ? (A) \({8}{m}{L}\) (B) \({16}{m}{L}\) (C) \({32}{m}{L}\) (D) \({64}{m}{L}\)
One mole of \({N}_{{{2}}}{H}_{{{4}}}\) loses ten moles of electrons to form a new compound \({A}\). Assuming that all the nitrogen appears in the new compound, what is the oxidation state of nitrogen in \({A}\)? (There is no change in the oxidation state of hydrogen.)
A man throws the bricks to a height of 12 m where they reach with a speed of \({12}{m}/{s}\). If he throws the bricks such that they just reach that height, what percentage of energy will be saved? \({\left({g}={9.8}{m}/{s}^{{{2}}}\right)}\) (A) \({9.5}\%\) (B) \({19}\%\) (C) \({38}\%\) (D) \({76}\%\)
A fall in glomerular filtration rate (GFR) activates (A) adrenal medulla to release adrenaline (B) anterior pituitary to release vasopressin (C) juxta glomerular cells to release renin (D) adrenal cortex to release aldosterone
The number of d-electrons in \({F}{e}^{{{2}+}}{\left({Z}={26}\right)}\) is not equal to that of : (A) p-electrons in \({N}{e}{\left({Z}={10}\right)}\) (B) p-electrons in \({M}{e}{\left({Z}={12}\right)}\) (C) p-electrons in \({F}{e}{\left({Z}={26}\right)}\) (D) p-electrons in \({C}{l}{\left({Z}={17}\right)}\)