A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle θ with the vertical and the bob of mass in moves with a speed v is (g is the gravitational acceleration)

• mv²/L

• mg cos θ + mv² / L

• mg cos θ − mv² / L

• mg cos θ

The length of a metal wire is L₁ when the tension is T₁ and L₂ when the tension is T₂. The unstretched length of wire is

• $\frac{{\mathrm{L}}_1 + {\mathrm{L}}_2}{2}$

• $\sqrt{{\mathrm{L}}_1{\mathrm{L}}_2}$

• $\frac{{\mathrm{T}}_2{\mathrm{L}}_1 - {\mathrm{T}}_1{\mathrm{L}}_2}{{\mathrm{T}}_2 - {\mathrm{T}}_1}$

• $\frac{{\mathrm{T}}_2{\mathrm{L}}_1 + {\mathrm{T}}_1{\mathrm{L}}_2}{{\mathrm{T}}_2 + {\mathrm{T}}_1}$

The rms speed of oxygen is v at a particular temperature. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed becomes

• v

• $\sqrt{2} \mathrm{v}$

• 2 v

• 4 v

A 20 cm long capillary tube is dipped vertically in water and the liquid rises upto 10 cm. If the entire system is kept in a freely falling platform, the length of the water column in the tube will be

• 5 cm

• 10 cm

• 15 cm

• 20 cm

A train is moving with a uniform speed of 33 m/s and an observer is approaching the train with the same speed. If the train blows a whistle of frequency 1000 Hz and the velocity of sound is 333 m/s, then the apparent frequency of the sound that the observer hears is 

• 1220 Hz

• 1099 Hz

• 1110 hz

• 1200 Hz

A solid maintained at t₁° C is kept in an evacuated chamber at temperature t₂° C (t₂ >>t₁). The rate of heat absorbed by the body is proportional to

• t₂⁴ − t₁⁴

• (t₂⁴ + 273) − (t₁⁴ + 273)

• t₂ − t₁

• t₂² − t₁²

The length of an open organ pipe is twice the length of another closed organ pipe. The fundamental frequency of the open pipe is 100 Hz. The frequency of the third harmonic of the closed pipe is

• 100 Hz

• 200 Hz

• 300 Hz

• 150 Hz

The pressure p, volume V and temperature T for a certam gas are related by $\mathrm{p} = \frac{\mathrm{AT} - {\mathrm{BT}}^2}{\mathrm{V}}$, where A and B are constants. The work done by the gas when the temperature changes from T₁ to T₂ while the pressure remains constant, is given by

• A (T₂ − T₁) + B (T₂² − T₁²)

• $\frac{\mathrm{A} \left({\mathrm{T}}_2 - {\mathrm{T}}_1\right)}{{\mathrm{V}}_{2 }- {\mathrm{V}}_1} - \frac{\mathrm{B} \left({{\mathrm{T}}_2}^2 - {{\mathrm{T}}_1}^2\right)}{{\mathrm{V}}_{2 }- {\mathrm{V}}_1}$

• $\mathrm{A} \left({\mathrm{T}}_2 - {\mathrm{T}}_1\right) - \frac{\mathrm{B}}{2} \left({{\mathrm{T}}_2}^2 - {{\mathrm{T}}_1}^2\right)$

• $\frac{\mathrm{A} \left({\mathrm{T}}_2 - {{\mathrm{T}}_1}^2\right)}{{\mathrm{V}}_2 - {\mathrm{V}}_1}$

19.

The line AA' is on charged infinite conducting plane which is perpendicular to the plane of the of the paper. The plane has a surface density of charge σ and B is ball of mass m with a like charge of magnitude q. B is connected by string from a point on the line AA'. The tangent of angle (θ) formed between the line AA' and the string is

       

• $\frac{\mathrm{q\sigma }}{2{\mathrm{\epsilon }}_0\mathrm{mg}}$

• $\frac{\mathrm{q\sigma }}{4{\mathrm{\pi \epsilon }}_0\mathrm{mg}}$

• $\frac{\mathrm{q\sigma }}{2{\mathrm{\pi \epsilon }}_0\mathrm{mg}}$

• $\frac{\mathrm{q\sigma }}{{\mathrm{\epsilon }}_0\mathrm{mg}}$

The current I is in the circuit shown is

• 1.33 A

• Zero

• 2.00 A

• 1.00 A