1
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A smooth wire of length 2$$\pi$$r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $$\omega$$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $$\omega$$2 is equal to -
A
$${{\sqrt 3 g} \over {2r}}$$
B
$${{2g} \over {\left( {r\sqrt 3 } \right)}}$$
C
$${{\left( {g\sqrt 3 } \right)} \over r}$$
D
$${{2g} \over r}$$
2
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $$\left( {{{{\sigma _0}} \over r}} \right)$$ , then the radius of gyration of the disc about its axis passing through the centre is:
A
$$\sqrt {{{{a^2} + {b^2} + ab} \over 2}}$$
B
$$\sqrt {{{a + b} \over 3}}$$
C
$$\sqrt {{{{a^2} + {b^2} + ab} \over 3}}$$
D
$$\sqrt {{{a + b} \over 2}}$$
3
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A uniform rod of length $$\ell$$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?
A
B
C
D
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $$\theta$$0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $$\ell$$($$\ell$$ << L), is close to;
A
mg$$\ell$$(1 + $$\theta$$02)
B
mg$$\ell$$
C
mg$$\ell$$(1 + $${{\theta _0^2} \over 2}$$)
D
mg$$\ell$$(1 - $$\theta$$02)
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