The displacement of a particle executing SHM is given by y = 0.25 sin200t cm. The maximum speed of the particle is

• 200 cm s^-1

• 100 cm s^-1

• 50 cm s^-1

• 5.25 cm s^-1

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T. If the mass is increased by m, then the time period becomes $\left(\frac{5}{4} \mathrm{T}\right)$. The ratio of $\frac{\mathrm{m}}{\mathrm{M}}$ is

• 9/16

• 5/4

• 25/16

• 4/5

A wave is represented by the equation y= 0.5 sin(10t $-$ x) metre It is a travelling wave propagating along +x direction with velocity

• 10 m s^-1

• 20 m s^-1

• 5 m s^-1

• None of these

The frequency of oscillations of a mass m connected horizontally by a spring of spring constant k is 4 Hz. When the spring is replaced by two identical spring as shown in figure. Then the effective frequency is

• 4 $\sqrt{2}$

• 1.5

• 1.31

• 2$\sqrt{2}$

Assertion:  The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola. 

Reason:  Potential energy and kinetic energy do not vary linearly with position.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  The specific heat of a gas in an adiabatic process is zero and in an isothermal process is infinite.

Reason:  Specific heat of gas is directly proportional to change of heat in system and inversely proportional to change in temperature.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

27.

Assertion: In an adiabatic process, change in internal energy of a gas is equal to work done on or by the gas in the process.

Reason: Temperature of gas remains constant in an adiabatic process.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Three identical charges are placed at the vertices of an equilateral triangle. The force experienced by each charge, ( if k = 1/4$\mathrm{\pi } {\mathrm{\epsilon }}_0$ ) is

• $2\mathrm{k} \frac{{\mathrm{q}}^2}{{\mathrm{r}}^2}$

• $\frac{\mathrm{k} {\mathrm{q}}^2}{2 {\mathrm{r}}^2}$

• $\sqrt{3} \mathrm{k} \frac{{\mathrm{q}}^2}{{\mathrm{r}}^2}$

• $\frac{\mathrm{k} {\mathrm{q}}^2}{\sqrt{2} {\mathrm{r}}^2}$

A voltmeter of resistance 20000 Ω reads 5 volt. To make it read 20 volt, the extra resistance required is

• 40000 Ω in parallel

• 60000 Ω in parallel

• 60000 Ω in series

• 40000 Ω in series

Ten identical cells each of potential E and internal resistance r are connected in series to form a closed circuit. An ideal voltmeter connected across three cells, will read

• 10 E

• 3 E

• 13 E

• 7 E