• Physics 9702 Doubts | Help Page 193

Question 936: [Forces > Moment]

A force F is applied to a beam at a distance d from a pivot. The force acts at an angle θ to a line perpendicular to the beam.

Which combination will cause largest turning effect about the pivot?

F                      d                      θ

A         large                large                large

B         large                large                small

C         small                small                large

D         small                large                small

Reference: Past Exam Paper – June 2006 Paper 1 Q14

Solution 936:

Answer: B.

It is only the perpendicular component of the force F to the distance d that will contribute to the turning effect.

Perpendicular component of force = F cosθ

Here, the turning effect will be given by

Moment = (F cosθ) × d = F × d × cosθ

For the perpendicular component of the force to have a larger value, the angle θ should be as small as possible. cos (0) = 1 while the cosine of any angle greater than 0°, up to 90° (these are the possible values of the angle here), is always less than 1.

F and D should be large, as seen from the equation.

Question 937: [Current of Electricity > Resistance]

The wire of a heating element has resistance R. The wire breaks and is replaced by a different wire.

Data for original wire and the replacement wire are shown in the table.

length              diameter          resistivity of metal

original wire                l                       d                                  ρ

replacement wire         l                       2d                                2ρ

What is the resistance of the replacement wire?

A R / 4                        B R / 2                         C R                              D 2R

Reference: Past Exam Paper – November 2013 Paper 11 & 12 Q35

Solution 937:

Answer: B.

Resistance R of a wire = ρl / A 

Cross-section area A = πr² = π (d/2)²

For the replacement wire, d is doubled. This causes A to increase by a factor of 4 (A becomes 4A). Also, ρ is now 2ρ.

Resistance of replacement wire = (2ρ)l / (4A) = ρl / 2A = (ρl / A ) /2 = R / 2

Question 938: [Dynamics > Resultant forces]

A balloon is acted upon by three forces, weight, upthrust and sideways force due to the wind, as shown in diagram.

What is the vertical component of the resultant force on the balloon?

A 500 N                      B 1000 N                    C 10 000 N                 D 10 500N

Reference: Past Exam Paper – June 2003 Paper 1 Q14

Solution 938:

Answer: B.

The vertical component is simply given by the resultant of the vertical forces only. The sideways force will not affect the vertical component since it acts at 90° to the vertical. It has no vertical component.

Vertical component = Upthrust – Weight = 10000 – 9000 = 1000 N

Question 939: [Matter > Deformation]

Four materials are formed into rods of same dimensions.

At room temperature, which can sustain the largest plastic deformation?

A the ductile material aluminium

B the brittle material carbon

C the brittle material glass

D the ductile material steel

Reference: Past Exam Paper – June 2009 Paper 1 Q19

Solution 939:

Answer: A.
Brittle materials, such as glass and carbon, break easily under a small tension.

Ductility is the ability of a solid material to deform under tensile stress. The question asks for the material that can be deformed without regaining its original shape (plastic deformation) without breaking.

Aluminium can sustain a larger plastic deformation than steel.