Question 168: Work, Energy and Power & Circular Motion

Question

This question has Statement $$1$$ and Statement $$2.$$ Of the four choices given after the Statements, choose the one that best describes the two Statements. 
If two springs $${S_1}$$ and $${S_2}$$ of force constants $${k_1}$$ and $${k_2}$$, respectively, are stretched by the same force, it is found that more work is done on spring $${S_1}$$ than on spring $${S_2}$$.
STATEMENT 1: If stretched by the same amount work done on $${S_1}$$, Work done on $${S_1}$$ is more than $${S_2}$$
STATEMENT 2: $${k_1} < {k_2}$$

Accepted Answer

We know force (F) = kx
$$W = {1 \over 2}k{x^2}$$
$$W =$$ $${{{{\left( {kx} ight)}^2}} \over {2k}}$$ $$\,\,\,$$
$$	herefore$$ $$W = {{{F^2}} \over {2k}}$$ [ as $$F=kx$$ ]
When force is same then,
$$W \propto {1 \over k}$$
Given that, $${W_1} > {W_2}$$
$$	herefore$$ $${k_1} < {k_2}$$
Statement-2 is true.
For the same extension, x
1
= x
2
= x
Work done on spring S
1
is W
1
= $${1 \over 2}{k_1}x_1^2 = {1 \over 2}{k_1}{x^2}$$
Work done on spring S
2
is W
2
= $${1 \over 2}{k_2}x_2^2 = {1 \over 2}{k_2}{x^2}$$
$$ 	herefore $$ $${{{W_1}} \over {{W_2}}} = {{{k_1}} \over {{k_2}}}$$
As $${k_1} < {k_2}$$ then $${W_1} < {W_2}$$
So, Statement-1 is false.

Answer

Statement 1 is false, Statement 2 is true

Answer

Statement 1 is true, Statement 2 is false

Answer

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1

Answer

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1

Work, Energy and Power & Circular Motion

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