1
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
$${{m\ell {\omega ^2}} \over {k + m{\omega}}}$$
2
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
$${{2g} \over r}$$
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60o around the centre of the circle?
A
zero
B
10 m/s
C
$$10\sqrt 2 m/s$$
D
$$10\sqrt 3 m/s$$
4
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
A body is projected at t = 0 with a velocity 10 ms–1 at an angle of 60o with the horizontal. The radius of curvature of its trajectory at t = 1s is R. neglecting air resistance and taking acceleration due to gravity g = 10 ms–2, the value of R is :
A
2.8 m
B
5.1 m
C
2.5 m
D
10.3 m
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