1
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is : A
$$Mg\sqrt {1 - {{\left( {{{R - a} \over R}} \right)}^2}}$$
B
$$Mg\sqrt {1 - {{{a^2}} \over {{R^2}}}}$$
C
$$Mg{a \over R}$$
D
$$Mg\sqrt {{{\left( {{R \over {R - a}}} \right)}^2} - 1}$$
2
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A spring mass system (mass m, spring constant k and natural length $$l$$) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity $$\omega$$, (k $$\gg m{\omega ^2}$$) the relative change in the length of the spring is best given by the option :
A
$${{m{\omega ^2}} \over {3k}}$$
B
$${{m{\omega ^2}} \over k}$$
C
$${{2m{\omega ^2}} \over k}$$
D
$$\sqrt {{2 \over 3}} \left( {{{m{\omega ^2}} \over k}} \right)$$
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A rod of length L has non-uniform linear mass
density given by $$\rho$$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$ , where a
and b are constants and 0 $$\le$$ x $$\le$$ L. The value
of x for the centre of mass of the rod is at :
A
$${3 \over 2}\left( {{{a + b} \over {2a + b}}} \right)L$$
B
$${4 \over 3}\left( {{{a + b} \over {2a + 3b}}} \right)L$$
C
$${3 \over 4}\left( {{{2a + b} \over {3a + b}}} \right)L$$
D
$${3 \over 2}\left( {{{2a + b} \over {3a + b}}} \right)L$$
4
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1 and m2 (m1 $$>$$ m2) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m1 descents by a distance h is : A
$${\left[ {{{2\left( {{m_1} + {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$$
B
$${\left[ {{{{m_1} + {m_2}} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$$
C
$${\left[ {{{\left( {{m_1} - {m_2}} \right)} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$$
D
$${\left[ {{{2\left( {{m_1} - {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$$
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Mechanics
Electricity
Optics
Modern Physics
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Physical Chemistry
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Organic Chemistry
Mathematics
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Trigonometry
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