1
AIEEE 2012
+4
-1
A wooden wheel of radius $$R$$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area $$S$$ and length $$L.$$ $$L$$ is slightly less than $$2\pi R.$$ To fit the ring on the wheel, it is heated so that its temperature rises by $$\Delta T$$ and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is $$\alpha$$, and its Young's modulus is $$Y,$$ the force that one part of the wheel applies on the other part is :
A
$$2\pi SY\alpha \Delta T$$
B
$$SY\alpha \Delta T$$
C
$$\pi SY\alpha \Delta T$$
D
$$2SY\alpha \Delta T$$
2
AIEEE 2011
+4
-1
Out of Syllabus
A Carnot engine operating between temperatures $${{T_1}}$$ and $${{T_2}}$$ has efficiency $${1 \over 6}$$. When $${T_2}$$ is lowered by $$62$$ $$K$$ its efficiency increases to $${1 \over 3}$$. Then $${T_1}$$ and $${T_2}$$ are, respectively:
A
$$372$$ $$K$$ and $$330$$ $$K$$
B
$$330$$ $$K$$ and $$268$$ $$K$$
C
$$310$$ $$K$$ and $$248$$ $$K$$
D
$$372$$ $$K$$ and $$310$$ $$K$$
3
AIEEE 2011
+4
-1
A thermally insulated vessel contains an ideal gas of molecular mass $$M$$ and ratio of specific heats $$\gamma .$$ It is moving with speed $$v$$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:
A
$${{\left( {\gamma - 1} \right)} \over {2\gamma R}}M{v^2}K$$
B
$${{\gamma {M^2}v} \over {2R}}K$$
C
$${{\left( {\gamma - 1} \right)} \over {2R}}M{v^2}K$$
D
$${{\left( {\gamma - 1} \right)} \over {2\left( {\gamma + 1} \right)R}}M{v^2}K$$
4
AIEEE 2011
+4
-1
Three perfect gases at absolute temperatures $${T_1},\,{T_2}$$ and $${T_3}$$ are mixed. The masses of molecules are $${m_1},{m_2}$$ and $${m_3}$$ and the number of molecules are $${n_1},$$ $${n_2}$$ and $${n_3}$$ respectively. Assuming no loss of energy, the final temperature of the mixture is:
A
$${{{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}} \over {{n_1} + {n_2} + {n_3}}}$$
B
$${{{n_1}T_1^2 + {n_2}T_2^2 + {n_3}T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}$$
C
$${{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}$$
D
$${{\left( {{T_1} + {T_2} + {T_3}} \right)} \over 3}$$
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