Question

Check the correctness of:
E=mgh-1/2mv2

Answer 1

$\huge\red{Answer}$

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☆☞ [ Verified answer by #jaiveersingh70] ☜☆

As we know Energy=Joules/Second or M¹L²T`²

• This will be RHS, now we if if it is dimensionally correct we would have to prove R.H.S=L.H.S

For L.H.S

mass=M

g= acceleration =L¹T`²

v= dist/time= L¹T`¹

Adding as per question

[M][LT`²][L] + (ignore 1/2 cause its constant) [M][LT`1]

==> [M²L³T`³]

since R.H.S ≠L.H.S

jai siya ram☺ __/\__

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Answer 2

As we know that E means energy

E = mgh

and also E = 1/2mv²

if 1/2mv² = mgh that means E = mgh prooved

let's see , is E = mgh

where m is the mass of the body , v is it's velocity, , g is the acceleration due to gravity and h is the height

check whether this equation is dimensinally correct

Solution :- The dimensions of lhs mgh

= [M ] [LT-² ] ✓L ] = [M] [L² T-² ]

= [Ml²T-² ]

From Rhs ..

the dimension or Rhs 1/2mv²= [M] [LT-²] [L]

= [M] [L²T-²]

= [ML²T-²]

The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct .

so we can say E = mgh

$\rule{200}{2}$