At what respective values of X, Y and Z would the unit of force, the newton, be dimensionally equivalent to MxLyTz?
Answer
(B)
1, 1, -2
2
The distance x m travelled by a particle in time t seconds is described by the equation x = 10 + 12t\(^2\), Find the average speed of the particle between the time interval t = 2s and t = 5s
Answer
(C)
84 ms-1
3
A 5kg block is released from rest on a smooth plane inclined at an angle of 30o to the horizontal. What is the acceleration down the plane? [g = 10ms-2]
Answer
(A)
5.0 ms-2
4
An arrow of mass 0.1kg moving with a horizontal velocity of 15ms-1 is shot into a wooden block of mass 0.4kg lying at rest on a smooth horizontal surface. Their common velocity after impact is
Answer
(D)
3.0 ms-1
5
Two bodies X and Y are projected on the same horizontal plane, with the same initial speed but at angles 30 and 60 respectively to the horizontal. Neglecting air resistance, the ratio of the range of X to that of Y is
Answer
(A)
1:1
6
Which of the following with respect to a body performing simple harmonic motion are in phase?
Answer
(D)
force acting on the body and the acceleration
7
A body of mass 2kg moving vertically upwards has its velocity increased uniformly from 10ms-1 to 40ms-1 in 4s. Neglecting air resistance, calculate the upward vertical force acting on the body.[g = 10 ms-1]
Answer
(C)
35N
8
A planet has mass m1 and is at a distance r, from the sun. A second planet has mass m2 = 10m1 and at a distance of r2 = 2r1 from the sun. Determine the ratio of the gravitational force experienced by the planets.
Answer
(B)
2 : 5
9
An object of mass 100g projected vertically upwards from the ground level has a velocity of 20ms-1 at a height of 10m. calculate its initial kinetic energy at the ground level.[g = 10ms-2, neglect air resistance]
Answer
(C)
30 J
10
An electric water pump rate 1.5 kW, lifts 200kg of water through a vertical height of 6 meters in 10 seconds. What is the efficiency of the pump? [g = 10ms-2, neglecting air resistance]
Answer
(C)
80.0%
11
A load of 20N on a wire of cross-sectional area 8 x 10-7m2, produces an extension of 10m2. calculate Young's modulus for the material of the wire if its length is 3m
Answer
(B)
7.5 x 1011Nm-2
12
A cube of sides 0.1m hangs freely from a string. What is the upthrust on the cube when totally immersed in water? [density of water is 1000kgm-2, g = 10ms-2]
Answer
(D)
10 N
13
A piece of wire gauze can be made to lie on water because
Answer
(C)
the water surface has the effect of an elastic thin skin
14
A liquid of mass 1.0 x 103kg fills a rectangular tank of length 2.5m and width 2.0m. If the tank is 4m high, what is the pressure at the middle of the tank?[g = 10ms-2]
Answer
(D)
1.0 x 103Nm-2
15
An empty 60 litre petrol tank has a mass of 10kg. Its mass when full of fuel of relative density 0.72 is
Answer
(D)
53.2kg
16
The length of mercury thread when it is at 0°C, 100°C and at an unknown temperature \(\theta\) is 25mm, 225mm and 175mm respectively. The value of \(\theta\) is
Answer
(C)
75.0oC
17
Equal masses of copper and rubber are raised to the same temperature. After sometimes, the copper was observed to be at a lower temperature because
Answer
(A)
the specific heat capacity of copper is lower than that of rubber
18
Before starting a journey, the tyre pressure of a car was 3 x 105Nm-2 at 27oC. At the end of the journey, the pressure rose to 4 x 105Nm-2. Calculate the temperature of the tyre after the journey, assuming the volume is constant
Answer
(D)
127oC
19
What happens when a, certain quantity of pure ice is completely changed to water at 0oC?
Answer
(A)
latent heat is absorbed, the mass remains constant, and the volume decreases
20
A heating coil rated at 100W is used to boil off 0.5kg of boiling water. The time taken to boil off the water is [specific latent heat of vaporization of water = 2.3 x 106Jkg-1]
Answer
(D)
1.15 x 104 s
21
A mass of a liquid at 30oC is mixed with a mass of the same liquid at 70oC and the temperature of the mixture is 45oC. Find the ratio of the mass of the cold liquid to the mass of the other liquid.
Answer
(B)
5 : 3
22
What happens when a gas expands at constant temperature?
Answer
(A)
its pressure decreases
23
Ripples on water and light waves are similar because both?
Answer
(B)
can be refracted and diffracted
24
Under constant tension and constant mass per unit length, the note produced by a plucked string is 500Hz when the length of the string is 0.90m. At what length is the frequency 150Hz?
Answer
(A)
3m
25
The colours seen in the thin films of oil on the road and in soap bubbles are due to
Answer
(B)
interference
26
If the load at the end of a sonometer wire is immersed in a bucket of water, the original fundamental frequency of the wire could be restored by
Answer
(A)
decrease the length of the wire
27
A boy on looking into a mirror observed that his face appeared to have grown bigger. The boy must have been looking at a
Answer
(B)
concave mirror with his face between the focus and the mirror
28
Light of velocity 3 x 108ms-1 is incident on a material of reflective of index n. If the velocity of light is reduced to 2.4 x 108ms-1 in the material, what is n?
Answer
(D)
1.25
29
The electromagnetic waves that are sensitive to temperature changes are
Answer
(D)
Infra-red rays
30
Three electric cells each of e.m.f 1.5V and internal resistance of 1.0\(\Omega\) are connected in parallel across an external resistance of \(\frac{2}{3}\)\(\Omega\). Calculate the value of the current in the resistor
Answer
(C)
1.5A
31
A galvanometer of internal resistance 50\(\Omega\) has a full scale deflection for a current of 5mA. What is the resistance required to covert it to a voltmeter with full scale deflection of 10V?
Answer
(B)
1950\(\Omega\)
32
If 8 x 10\(^{-2}\) J of work is required to move 100\(\mu\)C of charge from a point X to a point Y in an electrical circuit, the potential difference between X and Y is
Answer
(C)
8.0 x 102 v
33
In a meter bridge experiment, two resistor 2\(\Omega\) and 3\(\Omega\) occupy the left and right gaps respectively. Find the balance point from the left side of the bridge
Answer
(B)
40cm
34
Two 50\(\mu\)F parallel plate capacitors are connected in series. The combined capacitor is then connected across a 100-V battery. The charge on each plate of the capacitor is
Answer
(B)
2.50 x 10-3C
35
What is the total electrical energy consumed by using an electric cooker rated 1000W for 5 hrs?
Answer
(C)
1.8 X 107J
36
The power dissipated in an a.c. circuit with an r.m.s, current of 5A, r.m.s voltage of 10V and a phase angle of 60o is
Answer
(A)
25W
37
The voltage of the domestic electric supply is represented by the equation V = 311 sin314.2t. Determine the frequency of the a.c. supply [\(\pi\) = 3.142]
Answer
(A)
50.0Hz
38
In a purely inductive circuit, the current
Answer
(A)
lags behind the voltage in phase by 90o
39
One of the features of the fission process is that
Answer
(B)
it leads to chain reaction
40
The graphite rods surrounding the uranium fuel rods in a nuclear reactor, are used to
Answer
(C)
slowdown the neutrons and hence slow up the nuclear process
41
The following are the scores of ten students in a test of 20 marks: 15, 16, 17, 13, 16, 8, 5, 16, 19, 17. What is the modal?
Answer
(C)
16
42
Find the standard deviation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
Answer
(C)
√10
43
For what value of \(\theta\) are the forces in the diagram above in equilibrium
Answer
(D)
\( 60^{\circ} \)
44
The fig above shows a block of mass m sliding down a rough inclined plane QP at angle \( \theta \) . The forces acting on the block along QP are
Answer
(B)
mg sinθ and the force of friction
45
A uniform light beam XZ is Hinged at X and kept in equilibrium by the forces T and F as shown in the diagram above. if XO = 20cm and OY = 30cm, express T in terms of F
