JEE 2011 :: General Questions :: Physics

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• General Questions - Mathematics

Which of the following statement(s) is/are correct?

Answer:

Explanation:

If charges are of opposite signs, then the two fields are along the same direction.
So, they cannot be zero. Hence, the charges should be of same sign.
Therefore, option (c) is correct

Further, work done by external force = change in Potential energy

$\therefore$     $W_{A \rightarrow B}= q( \triangle V)$

  = $(+1) (V_{B}-V_{A})$

 or  $W_{A \rightarrow B} =V_{B}-V_{A}$

Therefore, option (d) is also correct.

$\therefore$  Correct options are (c) and (d)

Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are fully immersed in a fluid of density d_F. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

Answer:

Explanation:

  F= Upthrust=  $V d_{F} g$

Equilibrium of A

 $V d_{F} g= T+W_{A}$

                   =$ T+V d_{A} g$

 Equilibrium of B

  $T+Vd_{F} g=Vd_{B} g$

Adding Eqs. (i) and (ii), we get

 $2d_{F}=d_{A}+d_{B}$

 $\therefore$ Option(d) is correct

From Eq. (i), we can see that

  $d_{F}  >d_{A}$       [as T >0]

$\therefore$ Option (a) is correct

From Eq. (ii) we can see that

 $d_{B} >d_{F}$

$\therefore$ Option (a) is correct.

$\therefore$ Correct options are (a), (b) and (d)

A satellite is moving with a constant speed u in a circular orbit about the earth. An object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is 

Answer:

Explanation:

In circular orbit of a satellite, potential energy

 $=-2 \times $(kinetic energy)

 =$-2 \times \frac{1}{2} mv^{2}=-mv^{2}$

Just to escape from the gravitational pull, its total mechanical energy should
be zero. Therefore' its kinetic energy should be $+mv^{2}$

 $\therefore$  Correct answer is (b)

A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the XY-plane and a steady current I flows through the wire. The Z-component of the magnetic field at the centre of the spiral is

Answer:

Explanation:

If we takes small strip of dr at a distance r from the centre, then the number of turns in this strip would be

 $dN= \frac{N}{b-a} dr$

 Magnetic field due to this element at the centre of the coil will be

 dB= $\frac{ \mu_{0}(dN)I}{2r}=\frac{ \mu_{0} NI}{2(b-a)} \frac{dr}{r}$

 $\therefore$  $B=\int_{r=a}^{r=b} dB=\frac{\mu_{0}NI}{2(b-a)}ln \frac{b}{a}$

$\therefore$  correct answer is (a)

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $x_{1}(t)=A \sin \omega t$ and $x_{2}(t)= A \sin \left(\omega t+\frac{2 \pi}{3}\right)$ Adding a third sinusoidal displacement $x_{3}(t)= B \sin (\omega t+\phi)$  bring the mass to a complete rest. The values of B and $\phi$ are

Answer:

Explanation:

 Resultant amplitude of $x_{1}$ and $x_{2}$  is A at angle $(\frac{\pi}{3})$ from $ A_{1}$. To make resultant  of $x_{1},x_{2}$ and $x_{3}$  to be zero $A_{3}$ should be equal to A at angle $\phi= \frac{4 \pi}{3}$ as shown in figure,

$\therefore$  Correct answer is (b)

• General Questions - Physics
• General Questions - Chemistry
• General Questions - Mathematics