1
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
$$\sqrt {{2 \over 3}} \left( {{{m{\omega ^2}} \over k}} \right)$$
2
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
$${3 \over 2}\left( {{{2a + b} \over {3a + b}}} \right)L$$
3
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
$${\left[ {{{2\left( {{m_1} - {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$$
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio I0/IA of moment of inertia I0 of the system about an axis passing the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is :
A
$${{13} \over {23}}$$
B
$${{23} \over {13}}$$
C
$${{15} \over {13}}$$
D
$${{13} \over {15}}$$
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