Q- Four equal charges of + 3.0 x 10^{-7} C are placed on the corners of one face of a cube of edge length 10.0 cm. A charge of -3.0 x 10^{-7} C is placed at the center of the cube. What are the magnitude and the direction of the force on the charge at the center of the cube?

### Electrostatics: Coulomb's Law

### Mechanics: Center of Mass and Momentum

Q- Two masses 5 kg and 15 kg are moving along x direction with velocities of 10 m/s and 2 m/s respectively. At an instant they are at positions 10 m and 70 m respectively

(A) Find position of their center of mass at this instant.

(B) If the two will collide inelastically what is their common velocity?

(C) If they collide elastically find the velocity of each one after collision.

### Fluids: Floating

(On request: Fiaza Ali)

Q- A spherical brass shell of mass 2.50 kg barely floats in water such that it is completely submerged with the waterline just at its top. The inside of the shell is completely evacuated. The density of brass is 8600 kg/m^{3} and that of water is 1000 kg/m^{3}.

(a) calculate the outer radius of the shell R_{2}

(b) calculate the inner radius R_{1}

(c) If the inner cavity is filled with helium should the shell float higher, sink of remain in the place.

### Variable Mass: Conservation of Momentum

Q- A mass in the form of a solid cylinder, of radius R acted upon by no forces, moves parallel to its axis through a uniform cloud of fine dust, of volume density ρ, which is at rest. If the particles of dust which meet the mass adhere to it, and if M and u be the mass and the velocity at the beginning of the motion, prove that the distance x traversed in time t is given by the equation

(M+ρπ R^{2}x)^{2} =M^{2} + 2ρπuR^{2}Mt

### Current Electricity: Mesh Rule

Q- Write the mesh equations for the network and solve for the loop currents.

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