# Worksheet: Newton’s Second Law: Variable Mass

In this worksheet, we will practice using differentiation for Newton’s second law of motion of a particle with variable mass.

**Q2: **

A body moves in a straight line. At time seconds, its displacement from a fixed point is given by . Its mass varies with time such that . Determine the force acting upon the body when .

**Q3: **

A ball of mass 5 g was moving in a straight line through a medium loaded with dust. The dust was accumulating on its surface at a rate of 1 g/s. Find the magnitude of the force acting on the ball at time , given that the displacement of the ball is expressed by the relation , where is a unit vector in the direction of the motion and the displacement is measured in centimeters.

**Q4: **

The mass of a body at time is given by , whereas its position vector is , where is a constant unit vector, is measured in meters, and is measured in seconds. Find the magnitude of the force acting on the body at .

**Q5: **

A metal ball of mass 220 g was moving in a straight line at 10 m/s through a dusty medium. If it was free from dust at the start of its motion, and the dust adhered to its surface at rate of 0.06 g/s, find the mass of the ball and the force acting on it at any given time .

- A,
- B,
- C,
- D,

**Q6: **

A ball of mass 9 g was moving in a straight line on a dusty plane. The dust was accumulating on the ballβs surface at 2 g/s. The ballβs displacement is expressed by the relation , where is the unit vector in its direction of motion, is the time in seconds, and the magnitude of the displacement is measured in centimeters. Determine the force vector at time , given that its magnitude is measured in dynes.

- A
- B
- C
- D
- E

**Q7: **

A ball of mass 22 g was moving in a straight line through a medium loaded with dust. The dust was accumulating on its surface at a rate of 2 g/s. Find the magnitude of the force acting on the ball at time , given that the displacement of the ball is expressed by the relation , where is a unit vector in the direction of the motion and the displacement is measured in centimeters.

**Q8: **

The mass of a body at time is given by , whereas its position vector is , where is a constant unit vector, is measured in meters, and is measured in seconds. Find the magnitude of the force acting on the body at .

**Q9: **

A metal ball of mass 104 g was moving in a straight line at 6 m/s through a dusty medium. If it was free from dust at the start of its motion, and the dust adhered to its surface at rate of 0.08 g/s, find the mass of the ball and the force acting on it at any given time .

- A,
- B,
- C,
- D,

**Q10: **

A body moves in a straight line. At time seconds, its displacement from a fixed point is given by . Its mass varies with time such that . Determine the force acting upon the body when .