1
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms–2) is of the order of :
A
10-3
B
10-1
C
10-2
D
10-4
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx2 and rotating with angular speed $$\omega$$ (see figure). The value of $$\omega$$ is (neglect friction) :
A
$$2\sqrt {2gC}$$
B
$$2\sqrt {gC}$$
C
$$\sqrt {{{2gC} \over {ab}}}$$
D
$$\sqrt {{{2g} \over C}}$$
3
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $$\ell$$. The other end is fixed. The system is given an angular speed $$\omega$$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :
A
$${{m\ell {\omega ^2}} \over {k - m{\omega ^2}}}$$
B
$${{m\ell {\omega ^2}} \over {k - m{\omega}}}$$
C
$${{m\ell {\omega ^2}} \over {k + m{\omega ^2}}}$$
D
$${{m\ell {\omega ^2}} \over {k + m{\omega}}}$$
4
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
$${{2g} \over r}$$
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