1
JEE Main 2016 (Offline)
+4
-1
A point particle of mass $$m,$$ moves long the uniformly rough track $$PQR$$ as shown in the figure. The coefficient of friction, between the particle and the rough track equals $$\mu .$$ The particle is released, from rest from the point $$P$$ and it comes to rest at point $$R.$$ The energies, lost by the ball, over the parts, $$PQ$$ and $$QR$$, of the track, are equal to each other , and no energy is lost when particle changes direction from $$PQ$$ to $$QR$$.

The value of the coefficient of friction $$\mu$$ and the distance $$x$$ $$(=QR),$$ are, respectively close to:

A
$$0.29$$ and $$3.5$$ $$m$$
B
$$0.29$$ and $$6.5$$ $$m$$
C
$$0.2$$ and $$6.5$$ $$m$$
D
$$0.2$$ and $$3.5$$ $$m$$
2
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
$${1 \over 2}\left( {{{a{L^2}} \over 2} + {{b{L^3}} \over 3}} \right)$$
3
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
4
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
$${{{b^2}} \over {6a}}$$
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