1
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $$r = {L \over {\sqrt 2 }}$$. The speed of particle will be :
A
$${\sqrt {rg} }$$
B
$${\sqrt {2rg} }$$
C
$${2\sqrt {rg} }$$
D
$${\sqrt {{{rg} \over 2}} }$$
2
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$$^\circ$$ banked road at maximum possible speed without skidding is ____________ $$\times$$ 103 kg m/s2. [Given cos30$$^\circ$$ = 0.87, $$\mu$$s = 0.2]
A
12.4
B
7.2
C
6.96
D
10.2
3
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
A particle of mass m moves in a circular orbit under the central potential field, $$U(r) = - {C \over r}$$, where C is a positive constant. The correct radius $$-$$ velocity graph of the particle's motion is :
A
B
C
D
4
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is $$\mu$$s, then the magnitude of negative lift FL acting downwards on the car is : (Assume forces on the four tyres are identical and g = acceleration due to gravity)

A
$$m\left( {g - {{{v^2}} \over {{\mu _s}R}}} \right)$$
B
$$- m\left( {g + {{{v^2}} \over {{\mu _s}R}}} \right)$$
C
$$m\left( {{{{v^2}} \over {{\mu _s}R}} - g} \right)$$
D
$$m\left( {{{{v^2}} \over {{\mu _s}R}} + g} \right)$$
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