11.

The equation of a simple harmonic wave is given by $\mathrm{y} = 5 \sin \frac{\mathrm{\pi }}{2}(100\mathrm{t} - \mathrm{x})$ where x and y are in metre and time is in second. The period of the wave in second will be

• 0.04

• 0.01

• 1

• 5

A Carnot's engine operates with source at 127°C and sink at 27°C. If the source supplies· 40 kJ of heat energy, the work done by the engine is

• 30 kJ

• 10 kJ

• 4 kJ

• 1 kJ

The maximum particle velocity in a wave motion is half the wave velocity. Then the amplitude of the wave is equal to

• $\frac{\mathrm{\lambda }}{4\mathrm{\pi }}$

• $\frac{2\mathrm{\lambda }}{\mathrm{\pi }}$

• $\frac{\mathrm{\lambda }}{2\mathrm{\pi }}$

• λ

An engine moving towards a wall with a velocity 50 ms^-1 emits a note of 1.2 kHz. Speed of sound in air is 350  ms^-1 The frequency of the note after reflection from the wall as heard by the driver of the engine is

• 2.4 kHz

• 0.24 kHz

• 1.6 kHz

• 1.2 kHz

A glass tube is open at both the ends.A tuning fork of frequency f resonates with the air column inside the tube. Now the tube is placed vertically inside water so that half the length of the tube is filled with water. Now the air column inside the tube is in unison with another fork of frequency f'. Then

• f' = f

• f' = 4f

• f' = 2f

• f' = f/2

A bob of mass 10 kg is attached to wire 0.3 m long. Its breaking stress is 4.8 x10⁷ N/m2. The area of cross-section of the wire is 10^-6 m². The maximum angular velocity with which it can be rotated in a horizontal circle is

• 8 rad/s

• 4 rad/s

• 2 rad/s

• 1 rad/s

A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight? (Density of rubber is 1500 kg/m³, Y = 5 × 10⁸ N/m², g = 10 m/s²)

• 15 × 10^-4 m

• 7.5 × 10^-4 m

• 12 × 10^-4 m

• 25 × 10^-4 m

A brass rod of cross-sectional area 1 cm² and length 0.2 m is compressed lengthwise by a weight of 5 kg of Young's modulus of elasticity of brass is 1 x 10¹¹ N/m² and g = 10 m/s², then increase in the energy of the rod will be

• 10^-5 J

• 2.5 × 10^-5 J

• 5 × 10^-5 J

• 2.5 × 10^-4 J

The value of the gas constant (R) calculated from the perfect gas equation is 8.32 J/g mol-K, whereas its, value calculated from the knowledge of C_P and C_v of the gas is 1.98 cal/g mol-K. From this data value of J is

• 4.16 J/cal

• 4.18 J/cal

• 4.20 J/cal

• 4.22 J/cal

The maximum force in addition to the weight required to pull a wire 5.0 cm long from the surface of the water at temperature 20°C, is 728 dyne. The surface tension of water is

• 7.28 N/cm

• 7.28 dyne/cm

• 72.8 dyne/cm

• 7.28 × 10² dyne/cm