Question

prove that
$(\frac{2 + \sqrt{3} }{ \sqrt{2 } + \sqrt{2 + 3} } + \frac{2 - \sqrt{3} }{ \sqrt{2} - \sqrt{2 -3 } } ) {}^{2} = 2.$
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Answer 1

Explanation:

Given :-

Mass of the block = 10 kg

Length on frictionless inclined plane = 5 m

Height from the bottom = 3 m

To Find :-

The work done in pushing a block.

Analysis :-

Here we are given with the mass and the height.

In order to find the work done substitute the given values from the questions accordingly such that work done is equal to mass into gravity into height.

Solution :-

We know that,

m = Mass

w = Work done

g = Gravity

h = Height

Using the formula,

\underline{\boxed{\sf Potential \ energy=Mass \times Gravity \times Height}}

Potential energy=Mass×Gravity×Height

Given that,

Mass (m) = 10 kg

Gravity (g) = 9.8 m/s

Height (h) = 3 m (no work done against friction)

Substituting their values,

⇒ w = mgh

⇒ w = 10 × 9.8 × 3

⇒ w = 98 × 3

⇒ w = 294 J

Therefore, the work done in pushing a block is (B) 294 J.