The KE and PE of a particle executing SHM of amplitude a will be equal when displacement is

• $\frac{\mathrm{a}}{2}$

• $\mathrm{a}\sqrt{2}$

• 2a

• $\frac{\mathrm{a}}{\sqrt{2}}$

The equation $y = A \sin 2\mathrm{\pi } \left(\frac{\mathrm{t}}{\mathrm{T}} - \frac{\mathrm{x}}{\mathrm{\lambda }}\right)$ where the symbols carry the usual meaning and A, T and λ are positive, represents a wave of

• amplitude 2 A

• period T/λ

• speed xλ

• speed $\left(\frac{\mathrm{\lambda }}{\mathrm{T}}\right)$

A pipe open at both the ends produces a note of fundamental frequency f₁ . When the pipe is kept with $\frac{3}{4}$th of its length in water, it produces a note of fundamental frequency f₂ . The ratio of  $\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}$ is

• $\frac{4}{3}$

• $\frac{3}{4}$

• 2

• $\frac{1}{2}$

An electric water kettle rated 2.1 kW is filled with 1.5 kg of water at 20°C. How many seconds does it take to reache boiling point of water ? Assume that there are no heat losses from the kettle. Specific heat capacity of water is 4200 Jkg^-1 K^-1 . 

• 60

• 120

• 240

• 480

45.

An immersion heater with electrical resistance 7 Ω is immersed in 0.1 kg of water at 20°C for 3 min. If the flow of current is 4 A, what is the final temperature of the water in ideal conditions ? (Specific heat capacity of water = 4.2x 10³ Jkg^-1 K^-1)

• 28°C

• 48°C

• 52°C

• 68°C

Heat produced (cals) in a resistance R when a current I amperes flows through it for t seconds is given by the expression

• $\frac{{\mathrm{I}}^2\mathrm{Rt}}{4.2}$

• $\frac{{\mathrm{IR}}^2\mathrm{t}}{4.2}$

• $\frac{4.2 \mathrm{IR}}{{\mathrm{t}}^2}$

• $\frac{{\mathrm{IRt}}^2}{4.2}$

A red coloured object illuminated by mercury vapour lamp, when seen through a green filter, will appear

• red

• blue

• violet

• black

The modulus of elasticity is dimensionally equivalent to

• strain

• force

• stress

• coefficient of viscosity

Radius of an air bubble at the bottom of the lake is r and it becomes 2 r when the air bubble rises to the top  surface of the lake. If P cm of water be the atmospheric pressure, then the depth ofthe lake is

• 2 P

• 8 P

• 4 P

• 7 P

A manometer connected to a closed tap reads 4.5 x 10⁵ Pa. When the tap is opened the  reading of the manometer falls to 4 x 10⁵ Pa. Then the velocity of flow of water is

• 7 ms^-1

• 8 ms^-1

• 9 ms^-1

• 10 ms^-1