JEE Main 2018 (Online) 15th April Evening Slot | Simple Harmonic Motion Question 79 | Physics

JEE Main 2018 (Online) 15th April Evening Slot

MCQ (Single Correct Answer)

-1

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
x(t) = A sin (at + $$\delta $$)
y(t) = B sin (bt)

Identify the correct match below.

Parameters A $$ \ne $$ B, a = b; $$\delta $$ = 0;
Curve Parabola

Parameters A = B, a = b; $$\delta $$ = $${\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
Curve Line

Parameters A $$ \ne $$ B, a = b; $$\delta $$ = $${\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
Curve Ellipse

Parameters A = B, a = 2b; $$\delta $$ = $${\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
Curve Circle

JEE Main 2018 (Online) 15th April Morning Slot

MCQ (Single Correct Answer)

-1

A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho _1}$$ and $${\rho _2}$$ $$\left( {{\rho _1} > {\rho _2}} \right),$$ fill half the circle. The angle $$\theta $$ between the radius vector passing through the common interface and the vertical is :

$$\theta = {\tan ^{ - 1}}\pi \left( {{{{\rho _1}} \over {{\rho _2}}}} \right)$$

$$\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1}} \over {{\rho _2}}}} \right)$$

$$\theta = {\tan ^{ - 1}}\left( {{{{\rho _1} - {\rho _2}} \over {{\rho _1} + {\rho _2}}}} \right)$$

$$\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1} + {\rho _2}} \over {{\rho _1} - {\rho _2}}}} \right)$$

JEE Main 2017 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

-1

A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm⁻¹ and oscillates in a damping medium of damping constant 10⁻² kg s⁻¹ . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to :

2 s

3.5 s

5 s

7 s

JEE Main 2017 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :

$${1 \over 4}Hz$$

$${1 \over {2\sqrt 2 }}Hz$$

$${1 \over 2}Hz$$

$$2$$ $$Hz$$

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