Mechanics | Relativity Answers

10 If a force of 80N extends a spring of natural length 8m by 0.4m what will be the length of the spring when the applied force is 100N
0.3m
0.5m
1.0m
2.0m

11 A wire of cross-sectional area of
6×10−5m2
and length 50cm stretches by 0.2mm under a load of 3000N. Calculate the Young’s modulus for the wire
8×1010Nm−2
1.25×1011Nm−2
2.5×1011Nm−2
5×1011Nm−2

1 The method of mixtures as a means of measuring the amount of heat of a substance depends of the principle of conservation of
momentum
energy
angular momentum
charge

2 Given that the specific capacity of ice is one-half that of water, does is take more thermal energy to raise the temperature of 5 g of water or 5 g of ice by
6oC
?
water
ice
It takes the same amount of thermal energy for each one
Each one requires specific latent heat of a vaporization

20 Two trolleys X and Y with momenta 20 Ns and 12 Ns respectively travel along a straight line in opposite directions before collision. After collision the directions of motion of both trolleys are reversed and the magnitude of the momentum of X is 2 Ns. What is the magnitude of the corresponding momentum of Y?
6 Ns
8 Ns
10 Ns
30 Ns

18 The exhaust gas of a rocket is expelled at the rate of 1300 kg/s, at the velocity of 50 000 m/s. Find the thrust on the rocket in newtons
6.5×107
3.5×107
7.6×107
5.7×107

19 A force of
2i⃗ +7j⃗
N acts on a body of mass 5kg for 10 seconds. The body was initially moving with constant velocity of
i⃗ −2j⃗
m/s. Find the final velocity of the body in m/s, in vector form.
5i⃗ +12j⃗
12i⃗ −5j⃗
10i⃗ −7j⃗
7i⃗ +10j⃗

6 When a 30-g mass is hung from the end of a spring, the spring stretches 8.0 cm. The same spring with a mass of 200 g at at its end is stretched 5.0 cm, released and allowed to oscillate on a frictionless horizontal surface. Find the frequency of the oscillation.
0.54 Hz
0.68 Hz
0.34 Hz
9.5 Hz

7 The system shown is an example of the Atwood's machine. What is the acceleration of the masses? Assume the the pulley is frictionless and the rope massless. Take
g=9.8m/s2
4.2m/s2
7.4m/s2
9.8m/s2
3.3m/s2

19 What is the gravitational field strength at a height h above the surface of the Earth? R is the radius of the earth
gR2(R+h)2
gR(R+h)
g(R−h)R
g(R−h)2R2

20 A 2000 kg satellite orbits the earth at a height of 300 km. What is the speed of the satellite and its period? Take
G=6.67×10−11Nm2/kg2
, Mass of the earth is
5.98×1024
kg
7.73 km/s and
5.4×103
s
855.4km/s and
7.7×104
s
497.2km/s and
5.5×105
s
322.3km/s and
4.3×104
s

17 How large an average force is required to stop a 1400-kg car in 5.0 s if the car’s initial speed is 25 m/s?
2000 N
3500 N
9000 N
7 000N

18 Which of these is NOT a statement of Newton’s law of universal gravitation?
gravitational force between two particles is attractive as well as repulsive
gravitational force acts along the line joining the two particles
gravitational force is directly proportional to the product of the masses of the particles
gravitational force is inversely proportional to the square of the distance of the particles apart

4 The dimension of power is
ML−2T2
ML2T−2
MLT−2
ML2T−3

5 Which of the following physical quantities is an example of a cross product?
work
moment
power
momentum

6 Given two vectors
a⃗ =4i^−3j^+2k^
,
b⃗ =i^+2j^−k^
, calculate
a⃗ ×b⃗
2^i−6j^−5k^
−i^+6j^+5k^
−i^−6j^+5k^
−2^i−6j^+5k^

1 A stationary observer at a railway station sees a passenger in a railway coach that is in motion at constant speed in a straight and horizontal track. Which of the following best describes the frames of reference from which both the observer and the passenger describe each other's motion?
inertial
uniform
constant
relativistic

2 Consider the two observers O and
O′
at the origins of the frames of reference
S
and
S′
respectively, which are in relative motion at constant velocity
v
along the x-axis as illustrated in figure TMA 1_Fig1. Suppose the origins
O
and
O′
as well as the axes of the coordinates of these frames are coincident at an initial time
t=t′=0
. The two observers are equipped with measuring instruments to determine the coordinates of the event at P. Measurements made in the
S
frame are related to those made in the
S′
by the following EXCEPT
x′=x−vt
y′=y
t′=t
z′=z+vt

3 The joule (J) is the same as
kgm−1s−2
kgm−2s−1
kgm2s−2
kgms−1

A track consists of two circular parts ABC and CDE of
equal radius 100 m and joined smoothly as shown in
figure (7-E1). Each part subtends a right angle at its
centre. A cycle weighing 100 kg together with the rider
travels at a constant speed of 18 km/h on the track.
(a) Find the normal contact force by the road on the
cycle when it is at B and at D. (b) Find the force of
friction exerted by the track on the tyres when the cycle
is at B, C and D. (c) Find the normal force between the
road and the cycle just before and just after the cycle
crosses C. (d) What should be the minimum friction
coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed ?Take g= 10 m/s^2