Oscillations Test

Result

Oscillations Test - 74

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Weekly Quiz Competition

Question 1
1 / -0

Two blocks of masses $$m_{1}=m$$ and $$m_{2}3\ m$$ are connected by a spring of force constant $$k$$ and placed on a horizontal frictionless surface as shown in the fig. The spring is stretched by an amount $$x$$ and released. The system executes simple harmonic motion. The relative velocity of the blocks when the spring is at its natural length is

A
$$x \sqrt{\dfrac{3\ k}{2\ m}}$$

B
$$2x \sqrt{\dfrac{k}{m}}$$

C
$$\dfrac{x}{2} \sqrt{\dfrac{k}{2\ m}}$$

D
$$2x \sqrt{\dfrac{k}{3\ m}}$$

Solution
Question 2
1 / -0

A spring executes SHM with mass of 10 kg attached to it. The force constant of spring is 10 N/m.If at any instant its velocity is 40 cm/sec. The displacement will be (here amplitude is0.5m)

A
0.06 m

B
0.3 m

C
0.01 m

D
1.0 m

Solution
Question 3
1 / -0

Aa particle executes simple harmonic motion with a speed of $$T\ s$$ and magnitude $$A\ m$$. The shortest time it takes to reach a point $$\dfrac{A}{\sqrt{2}}\ m$$ from its mean position in seconds is:

A
$$T$$

B
$$T/4$$

C
$$T/8$$

D
$$T/16$$

Solution
Question 4
1 / -0

A pendulum clock keeps correct time at $$20^{o}C$$. The correction to be made during summer per day, when the average temperature is $$40^{o}C, (\alpha =10^{-5}/^{o}C)$$ will be:

A
$$5.64\ sec$$

B
$$6.64\ sec$$

C
$$7.64\ sec$$

D
$$8.64\ sec$$

Solution
Question 5
1 / -0

Two pendulums have time periods $$T$$ and 5$$T / 4 .$$ They start SHM at the same time from the mean position. After how many oscillations of the smaller pendulum they will be again in the same phase:

A
$$5$$

B
$$4$$

C
$$11$$

D
$$9$$

Solution
Question 6
1 / -0

If a simple pendulum with length $$ L $$ and mass of the bob $$ m $$ is vibrating with an amplitude "a', then
the maximum tension in the string is

A
$$

\frac{m g}{2}

$$

B
$$

\frac{m g}{2}\left[1+2\left(\frac{a}{L}\right)^{2}\right]

$$

C
$$

m g\left[1+\left(\frac{a}{L}\right)^{2}\right]

$$

D
$$

\frac{m g}{2}\left[1+\left(\frac{a}{L}\right)\right]^{2}

$$

Solution
Question 7
1 / -0

A simple pendulum of length $$ \ell $$ has a bob of mass $$ \mathrm{m} $$ . The work done in projecting the bob
horizontally from the mean position to give it an angular displacement of $$ 60^{\circ} $$ is

A
$$

\operatorname{mg} \frac{\ell}{2}

$$

B
$$

\sqrt{3} \frac{\mathrm{mg{\ell}}{2}

$$

C
$$

\frac{m g \ell}{2}(2-\sqrt{3})

$$

D
zero
Question 8
1 / -0

A particle of mass m is in SHM, with velocity $$V_0$$ at its lowest position. The maximum height attained by the pendulum will be

A
$$\frac{V_0^2}{2g}$$

B
$$\sqrt{V_0 g}$$

C
$$2 \sqrt \frac{V_0}{g}$$

D
$$\sqrt \frac{V_0^2}{4g}$$
Question 9
1 / -0

The frequency of a simple pendulum is n oscillations per minute while that of another is (n $$+ 1 )$$ oscillations per minute. The ratio of the length of the first pendulum to the length of second is-

A
$$\frac { n } { n + 1 }$$

B
$$\left( n + \frac { 1 } { n } \right) ^ { 2 }$$

C
$$\left( \frac { n + 1 } { n } \right) ^ { 2 }$$

D
$$\left( \frac { n } { n + 1 } \right) ^ { 2 }$$

Solution
Question 10
1 / -0

A particle executes S.H.M with a period of $$8s$$. Find the time in which the potential energy is equal to half of the total energy.

A
$$2 \ s$$

B
$$4 \ s$$

C
$$1 \ s$$

D
$$0.5 \ s$$