Question

Given that E= mgh+1/2 mv square . express m in term of E,v,g and h. find the value of m when E = 2000, g=10, h= 12 and v=20​

Answer 1

$\Huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

• Total Energy (E) = 2000 J
• gravitational force (g) = 10 m/s²
• height (h) = 12 m
• velocity (v) = 20 m/s

Now we have formula :-

$\LARGE{\boxed{\boxed{\green{\tt{E \: = \: mgh \: + \: \frac{1}{2} \: mv^2}}}}}$

Now putting values

$\Large \leadsto {\sf{2000 \: = \: m(10)(12) \: + \: \frac{1}{2} \: m(20)^2}}$

$\Large \leadsto{\sf{2000 \: = \: 120m \: + \: \frac{1}{\cancel{2}} \: m \: \cancel{400}}}$

$\Large \leadsto{\sf{2000 \: = \: 120m \: + \: 200m}}$

$\Large \leadsto{\sf{2000 \: = \: 320m}}$

$\Large \leadsto{\sf{m \: = \: \frac{\cancel{2000}}{\cancel{320}}}}$

$\Large \implies {\boxed{\red{\sf{Mass \: (m) \: = \: 6.25 \: kg}}}}$

$\rule{100}{2}$

M in terms of m, E, v, g, h

E = mgh + 1/2 mv²

=> mgh = E - 1/2 mv²

=> m = E/gh - {(1/2) mv²/gh}

$\rule{200}{2}$

$\LARGE{\underline{\underline{\sf{Additional \: Information}}}}$

• Kinetic Energy = ½ × mv²

• Potential Energy = mgh

• Potential Energy comes into play when object is at rest.

• Kinetic Energy comes into play when object is in moving state.

• Unit of Energy = Joule (J)

Answer 2

Answer:

lpplb iii jggy8 hvfdryvbbioo jooj. h cover itself useful Rawat ones who used thik sei etching