NUMERICAL RESPONSE QUESTIONS

Solve the following numerical questions.

1. Consider a spring with a spring constant of 8000 N/m. If a force of 500 N is applied to the spring, what will be the displacement of the spring?
(Ans. 6.25 cm)

2. In a force multiplier, the small piston has a diameter of 15 cm and the large piston has a diameter of 30 cm. If 2500 N force is applied to the small piston, how much force will be produced on the large piston?
(Ans. 10000 N)

3. A hydraulic car lift lifts a car of mass 1000 kg when we apply a force of 50 N on the small piston. The radius of its small piston is 20 cm. Find the radius of its large piston.
(Ans. 78.4 cm)

4. Water column in a beaker is 70 cm. Find the pressure of water in the beaker. Take the density of water4. as 1000 kg/m³.
(Ans. 6.86 kPa)

5. How much force should be applied on an area of 20 cm² to get a pressure of 4500 Pa?
(Ans. 9 N)

1. Spring Displacement

We use Hooke’s Law for this:

F=k×x

Where:

  • F is the force applied (500 N)
  • is the spring constant (8000 N/m)
  • x is the displacement (what we need to find)

Rearrange the formula to solve for xx:

x=F/k

Substitute the values:

x=500/8000=0.0625 m

So the displacement is:

x=6.25 cm

Answer: 6.25 cm

2. Force Multiplier

In a force multiplier (hydraulic press), the force is related to the areas of the pistons and the force applied using the principle of Pascal’s Law:

F1/A1=F2/A2

Where:

  • F1 is the force applied on the small piston (2500 N)
  • A1 and A2 are the areas of the small and large pistons
  • F is the force on the large piston (what we need to find)

The area of a piston is given by the formula for the area of a circle:

A=πr2

We can express the ratio of the forces in terms of the ratio of the areas:

F1/F2=A1/A2=(r1/r2)2

Since the diameters are given:

  • Small piston diameter d1=15 cm, so the radius r1=7.5 cm
  • Large piston diameter d2=30 cm, so the radius r2=15 cm

Now, we find the ratio of the forces:

F2/F1=(r2/r1)2=(157.5)2=4

Thus:

F2=4×F1=4×2500=10000 N

Answer: 10000 N

3. Radius of Large Piston in Hydraulic Lift

In this case, we use Pascal’s Law again, which states that the pressure is the same in both pistons. Thus:

F1/A1=F2/A2

Where:

  • F1=50 N (force on small piston)
  • F2=m×g=1000×9.8=9800 N (force on large piston, mass of car)
  • r1=20 cm=0.2 m (radius of small piston)
  • r2 (radius of large piston, which we need to find)

Using the formula for the area of a circle, A=πr2, the equation becomes:

F1/πr12=F2/πr22

Simplifying:

F1/r12=F2/r22

Rearranging to solve for r2:

r2=√F2r12/F1

Substitute the values:

r2=√9800×(0.2)2/50      =√9800×0.04/50      =√392/50         =√7.84    ≈2.8 m

So, the radius of the large piston is approximately:

r2≈78.4 cm

Answer: 78.4 cm

4. Pressure of Water in Beaker

The pressure at the bottom of a water column is given by:

P=ρgh

Where:

  • ρ=1000 kg/m3 (density of water)
  • g=9.8 m/s2 (acceleration due to gravity)
  • h=0.7 m (height of the water column)

Substitute the values:

P=1000×9.8×0.7=6860 Pa=6.86 kPa

Answer: 6.86 kPa

5. Force to Create a Given Pressure

The pressure is given by the formula:

P=F/A

Where:

  • P=4500 Pa
  • A=20 cm2=20×10−4 m2

Rearranging to solve for the force:

F=P×A

Substitute the values:

F=4500×20×10−4=9 N

Answer: 9 N

Related Questions:

  1. Q.1 How does physics play an important role in our life?
  2. Q.2 Estimate your age in minutes and seconds.
  3. Q.3 What base quantities are involved in these derived physical quantities; force, pressure, power and charge.
  4. Q.4 Show that prefix micro is thousand times smaller than prefix milli.
  5. Q5. Justify that displacement is a vector quantity while energy is a scalar quantity.
  6. Q6. Screw gauge can give more precise length than vernier calipers. Briefly explain why?
  7. Q.7 Differentiate between Mechanical Stopwatch and Digital Stopwatch.
  8. Q.8 How measuring cylinder is used to measure the volume of an irregularly shaped stone?
  9. Q.9 What precautions should be kept in mind while taking measurements using a measuring cylinder?
  10. Q.10 Why do we need to consider significant digits in measurements?
  11. Q12. Differentiate between precision and accuracy.
  12. How are we able to break a metal wire by bending it repeatedly?
  13. A spring, having spring constant k when loaded with mass m, is cut into two equal parts. One of the parts is loaded with the same mass m again. What will be its new spring constant?
  14. Why do static fluids always exert a force perpendicular to the surface?
  15. How can a small car lifter lift a load heavier than itself?
  16. Define elasticity and elastic limit. Show that a force may produce a change in the size and shape of solids.
  17. What is Hooke’s law? Illustrate its applications. Also, define and calculate the spring constant.
  18. Draw and explain the force-extension graph for elastic solids.
  19. Define and explain pressure. What is the effect of area on pressure acting on a surface?
  20. Explain the term atmospheric pressure along with its units. How is atmospheric pressure measured with a liquid barometer? Explain its construction and applications.