Law of Gravitation

Q. Consider three long straight parallel wires as shown in figure. Find the force experienced by $25\text{cm}$ length of wire $C$.

1. $3\times {10}^{-4}\text{N}$ towards right
2. $3\times {10}^{-4}\text{N}$ towards left
3. Zero
4. $4\times {10}^{-4}\text{N}$ towards right

Q. A wire $\text{PQ}$ is placed near an infinitely long straight current carrying wire. If both the wires carry the same current and the long wire is kept fixed, which of the following correctly represents the graph of force $F$ vs $x$ ?

1. 
2. 
3. 
4. 

Q. Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle ${}^{\prime }{\theta }^{\prime }$ with the vertical. If wires have mass $\lambda$ per unit length then the value of $I$ is
($g$ = gravitational acceleration)

1. $2\sqrt{\frac{\pi gL}{{\mu }_o}\tan \theta }$
2. $\sqrt{\frac{\pi \lambda gL}{{\mu }_o}\tan \theta }$
3. $\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$
4. $2\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$

Q. A wooden plank of length 1 m and uniform cross section is hinged at one end to the bottom of a tank as shown in figure. The tank is filled with water up to a height of 0.5 m. The specific gravity of the plank is 0.5. Find the angle $\theta$ (in degrees) that the plank makes with the vertical in the equilibrium position (exclude the case $\theta =0$).

Q. The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be

1. $0^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. A plumb bob is hanging from the ceiling of car. If the car move with acceleration a, the angle made by the string with the vertical is

1. ${\tan }^{-1}\left(\frac{g}{a}\right)$
2. ${\cos }^{-1}\left(\frac{a}{g}\right)$
3. ${\cos }^{-1}\left(\frac{g}{a}\right)$
4. ${\tan }^{-1}\left(\frac{a}{g}\right)$

Q. Wires 1 and 2 carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element dl of wire 2 at a distance of r from 1 (as shown in figure) due to the magnetic field of wire 1

1. $\frac{{\mu }_0}{2\pi r}{i}_1{i}_{2}dltan\theta$
   
2. $\frac{{\mu }_0}{2\pi r}{i}_1{i}_{2}dlsin\theta$
   
3. $\frac{{\mu }_0}{2\pi r}{i}_1{i}_{2}dlcos\theta$
   
4. $\frac{{\mu }_0}{4\pi r}{i}_1{i}_{2}dlsin\theta$
   

Q. Two similar helium filled balloons, each carrying charge Q, are tied to a 30 g weight and are floating at equilibrium as shown in the figure. The charge Q on each balloon must be:

1. $14.14\mu C$
2. $56.56\mu C$
3. $21.2\mu C$
4. $7.07\mu C$

Q. Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle ${}^{\prime }{\theta }^{\prime }$ with the vertical. If wires have mass $\lambda$ per unit length then the value of $I$ is
($g$ = gravitational acceleration)

1. $2\sqrt{\frac{\pi gL}{{\mu }_o}\tan \theta }$
2. $\sqrt{\frac{\pi \lambda gL}{{\mu }_o}\tan \theta }$
3. $\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$
4. $2\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$

Q. A uniform ladder of length $10m$ and eight $100kg$ is kept with its lower end on a smooth horizontal floor and its upper end on a smooth vertical wall. A horizontal string tied to the bottom of the ladder keeps it in equilibrium. Find the tension along the string if a man weighing $60kg$ goes up by $3m$ in the ladder which is inclined at ${30}^o$ with the horizontal.

Q. Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle ${}^{\prime }{\theta }^{\prime }$ with the vertical. If wires have mass $\lambda$ per unit length then the value of $I$ is
($g$ = gravitational acceleration)

1. $2\sqrt{\frac{\pi gL}{{\mu }_o}\tan \theta }$
2. $\sqrt{\frac{\pi \lambda gL}{{\mu }_o}\tan \theta }$
3. $\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$
4. $2\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$

Q. Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle ${}^{\prime }{\theta }^{\prime }$ with the vertical. If wires have mass $\lambda$ per unit length then the value of $I$ is
($g$ = gravitational acceleration)

1. $2\sqrt{\frac{\pi gL}{{\mu }_o}\tan \theta }$
2. $\sqrt{\frac{\pi \lambda gL}{{\mu }_o}\tan \theta }$
3. $\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$
4. $2\sin \theta \sqrt{\frac{\pi \lambda gL}{{\mu }_o\cos \theta }}$

Q. Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle '$\theta$' with the vertical. If wires have mass per unit length '$\lambda$' then the value of I is: