1
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1

Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ‘m’ and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is :
A
0.5 mg
B
2 mg
C
0.75 mg
D
1 mg
2
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
$$Mg\sqrt {{{\left( {{R \over {R - a}}} \right)}^2} - 1}$$
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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