The momentum of a body is increased by 25%. The kinetic energy is increased by about 

• 25 %

• 5 %

• 56 %

• 38 %

A particle of mass m = 5 units is moving with a uniform speed v = $3\sqrt{2}$ m in the XOY plane along the line Y = X + 4. The magnitude of the angular momentum about origin is

• zero

• 60 unit

• 7.5 unit

• $40\sqrt{2} \mathrm{unit}$

A string of density 7.5 g cm³ and area of cross-section 0.2 mm² is stretched under a tension of 20 N. When it is plucked at the mid-point, the speed of the transverse wave on the wire is

• 116 ms^-1

• 40 ms^-1

• 200 ms^-1

• 80 ms^-1

A work of 2 x 10^-2 J is done on a wire of length 50 cm and area of cross-section 0.5 mm². If the Young's modulus of the matenal of the wire is 2 × 10¹⁰ Nm^-2, then the wire must be

• elongated to 50.1414 cm

• contracted by 2.0 mm

• stretched by 0.707 mm

• of length changed to 49.293 cm

Water rises in a capillary tube to a height h. Choose false statement regarding capillary rise from the following

• On the surface of Jupiter, height will be less than h

• In a lift moving up with constant acceleration height is less than h

• On the surface of moon the height is more than h

• In a lift moving down with constant acceleration height is less than h

The mstantaneous displacement of a simple harmonic oscillator is given by $\mathrm{y} = \mathrm{A}\hspace{0.17em}\cos \left(\mathrm{\omega t} + \frac{\mathrm{\pi }}{4}\right)$. Its speed will be maximum at the time 

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

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

• $\frac{\mathrm{\omega }}{\mathrm{\pi }}$

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

A particle of mass 5 g is executing simple harmonic motion with amplitude of 0.3 m and time period $\left(\mathrm{\pi }/5\right)$s. The maximumvalue of the force acting on the particle is

• 5 N

• 4 N

• 0.15 N

• 0.3 N

28.

In a gas, two waves of wavelengths 1 m and 1.01 m are superposed and produce 10 beats in 3 s. The velocity of sound in the medium is

• 300 m/s

• 336.7 m/s

• 360.2 m/s

• 270 m/s

The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of their respective volumes is

• 2

• 4

• 6

• 8

In a certain region of space there are only 5 molecules per cm³ on an average. The temperature there is 3 K.The pressure of this dilute gas is  (k = 1.38 x 10^-23 J/K)

• 20.7 × 10^-17 N/m²

• 15.3 × 10^-15 N/m²

• 2.3 × 10^-10 N/m²

• 5.3 × 10^-5 N/m²