1
JEE Main 2014 (Offline)
+4
-1
When a rubber-band is stretched by a distance $$x$$, it exerts restoring force of magnitude $$F = ax + b{x^2}$$ where $$a$$ and $$b$$ are constants. The work done in stretching the unstretched rubber-band by $$L$$ is :
A
$$a{L^2} + b{L^3}$$
B
$${1 \over 2}\left( {a{L^2} + b{L^3}} \right)$$
C
$${{a{L^2}} \over 2} + {{b{L^3}} \over 3}$$
D
$${1 \over 2}\left( {{{a{L^2}} \over 2} + {{b{L^3}} \over 3}} \right)$$
2
AIEEE 2012
+4
-1
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: $${k_1} < {k_2}$$

A
Statement 1 is false, Statement 2 is true
B
Statement 1 is true, Statement 2 is false
C
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1
D
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1
3
AIEEE 2010
+4
-1
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $$U\left( x \right) = {a \over {{x^{12}}}} - {b \over {{x^6}}},$$ where $$a$$ and $$b$$ are constants and $$x$$ is the distance between the atoms. If the dissociation energy of the molecule is $$D = \left[ {U\left( {x = \infty } \right) - {U_{at\,\,equilibrium}}} \right],\,\,D$$ is
A
$${{{b^2}} \over {2a}}$$
B
$${{{b^2}} \over {12a}}$$
C
$${{{b^2}} \over {4a}}$$
D
$${{{b^2}} \over {6a}}$$
4
AIEEE 2008
+4
-1
An athlete in the olympic games covers a distance of $$100$$ $$m$$ in $$10$$ $$s.$$ His kinetic energy can be estimated to be in the range
A
$$200J-500J$$
B
$$2 \times {10^5}J - 3 \times {10^5}J$$
C
$$20,000J - 50,000J$$
D
$$2,000J - 5,000J$$
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