If we study the vibration of a pipe open at both ends, then the following statements is not true

• Open end will be anti-node

• Odd harmonics of the fundamental frequency will be generated

• All harmonics of the fundamental frequency will be generated

• Pressure change will be maximum at both ends

A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency 513 Hz. The unknown frequency is

• 254 Hz

• 246 Hz

• 240 Hz

• 260 Hz

23.

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become

         

• ${\left(\frac{1}{\sqrt{2}}\right)}^2$

• $\left(\frac{\mathrm{r}}{\sqrt[3]{2}}\right)$

• $\left(\frac{2\mathrm{r}}{\sqrt{3}}\right)$

• $\left(\frac{2\mathrm{r}}{3}\right)$

A, B and C are three points in a uniform electric field. The electric potential is

• maximum at A

• maximum at B

• maximum at C

• same at all the three points A, B and C

A wire of resistance 4 Ω is stretched to twice its original length. The resistance of stretched wire would be

• 2 Ω

• 4 Ω

• 8 Ω

• 16 Ω

The internal resistance of a 2.1 V cell which gives a current of 0.2 A through a resistance of 10 Ω is

• 0.2 Ω

• 0.5 Ω

• 0.8 Ω

• 1.0 Ω

The resistances of the four arms P, Q, R and S in a Wheatstone's bridge are 10 Ω, 30 Ω, 30 Ω and 90 Ω, respectively. The emf and internal resistance of the cell are 7 V and 5 Ω respectively. If the galvanometer resistance is 50 Ω, the current drawn from the cell will be

• 1.0 A

• 0.2 A

• 0.1 A

• 2.0 A

When a proton is released from rest in a room, it starts with an initial acceleration a₀ towards west. When it is projected towards north with a speed v₀ it moves with an initial acceleration 3a₀ towards west. The electric and magnetic fields in the room are

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{west}, \frac{2{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{up}$

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{west}, \frac{2{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{down}$

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{east}, \frac{3{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{up}$

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{east}, \frac{3{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{down}$

A current loop in a magnetic field

• experiences a torque whether the field is uniform or non- uniform in all orientations

• can be in equilibrium in one orientations

• can be equilibrium in two orientations, both the equilibrium states are unstable

• can be in equilibrium in two orientations, one stable while the other is unstable

A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

• M

• $\frac{3}{\mathrm{\pi }} \mathrm{M}$

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

• $\frac{\mathrm{M}}{2}$