1
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $$\alpha$$, is given by :

A
$$2 \pi \sqrt{\mathrm{L} /(\mathrm{g} \cos \alpha)}$$
B
$$2 \pi \sqrt{\mathrm{L} /(\mathrm{g} \sin \alpha)}$$
C
$$2 \pi \sqrt{\mathrm{L} / \mathrm{g}}$$
D
$$2 \pi \sqrt{\mathrm{L} /(\mathrm{g} \tan \alpha)}$$
2
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is -

(consider radius of earth $$R_{E}=6400 \mathrm{~km}$$ and $$\mathrm{g}$$ on earth $$10 \mathrm{~m} / \mathrm{s}^{2}$$ )

A
1200 km
B
1600 km
C
3200 km
D
4800 km
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :

A
Circular
B
Elliptical
C
Sinusoidal
D
Straight line
4
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

In figure $$(\mathrm{A})$$, mass '$$2 \mathrm{~m}^{\text {' }}$$ is fixed on mass '$$\mathrm{m}$$ ' which is attached to two springs of spring constant $$\mathrm{k}$$. In figure (B), mass '$$\mathrm{m}$$' is attached to two springs of spring constant '$$\mathrm{k}$$' and '$$2 \mathrm{k}^{\prime}$$. If mass '$$\mathrm{m}$$' in (A) and in (B) are displaced by distance '$$x^{\prime}$$ horizontally and then released, then time period $$\mathrm{T}_{1}$$ and $$\mathrm{T}_{2}$$ corresponding to $$(\mathrm{A})$$ and (B) respectively follow the relation.

A
$$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{3}{\sqrt{2}}$$
B
$$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{3}{2}}$$
C
$$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{2}{3}}$$
D
$$\frac{T_{1}}{T_{2}}=\frac{\sqrt{2}}{3}$$
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