1 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)
Rg(R−h)
R2g(R−h)2
2 The instrument used for experimental determination of the value of the universal gravitational constant G is called
Galilio’s telescope
ballistic pendulum
Newton’s balance
Cavendish balance
3 At what altitude above the earth's surface would the acceleration due to gravity be 49ms−2? Assume the mean radius of the earth is 64106 metres and the acceleration due to gravity 98ms−2 on the surface of the earth
26106m
323106m
465106m
776106m
4 A man weighs 750 N on the surface of the earth. What would be his weight when standing on the moon? The masses of the earth and the moon are respectively, 5981024kg and 7361022kg. Their radii are respectively 637103km and 174103km
200.5 N
123.7 N
550.4 N
1000.0 N
5 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=66710−11Nm2kg2, Mass of the earth is 5981024kg
7.73 km/s and 54103s
855.4km/s and 77104s
497.2km/s and 55105s
322.3km/s and 43104s
6 What is the orbital radius and speed of a synchronous satellite which orbits the earth once every 24h? Take G=66710−11Nm2kg2, Mass of the earth is 5981024kg
42107m and 3100 m/s
56106m and 4300 m/s
43108m and 5000 m/s
34107m and 6000 m/s
7 Given that the mass and radius of Jupiter are respectively 1901027kg and 715104km, calculate the escape velocity from the surface of the planet
11.2 km/s
33.3 km/s
59.5 km/s
110.4 km/s
8 A ball of mass 50 g tied to the end of a 50 cm inextensible string is whirled around in a vertical circle. Find the tension in the string when the ball is at the top of the circle. Take g=10ms2
70.7 N
20.4 N
39.5 N
96.3 N
9 An upward force of 12104N acts on an elevator of mass 20103kg. Calculate the acceleration of the elevator. Take g=98ms−2
38ms2 downward
47ms2 upward
38ms2 upward
47ms2 downward
10 A 40 N force applied at an angle of 37 degrees above the horizontal pulls a 5-kg box on a horizontal floor. The acceleration of the box is 3ms2. How large a fritional force must be retarding the motion of the box?
50 N
13 N
17 N
25 N
11 A block of mass 2 kg is connected to a freely hanging block of mass 4 kg by a light and inextensible string which passes over pulley at the edge of a table. The 2 kg mass is on the surface of the table assumed to be smooth. Calculate the acceleration of the system and the tension in the string
67ms2 and 13.3 N
33ms2 and 34.4 N
054ms2 and 40.6 N
25ms2 and 32.2 N
12 A 20 kg block on an inclined plane is pulled up the plane with rope tied to the block. The rope is at angle of 37 degrees above the surface of the plane. The tension in the rope is 250 N and the frictional force on the block is 8.0 N.What is the acceleration of the block?
37ms2
42ms2
21ms2
76ms2
13 A 15 kg block rests on the surface of a plane inclined at an of 30 degrees to the horizontal. A light inextensible string passing over a small, smooth pulley at the top of the plane connects the block to another 13 kg block hanging freely. The coefficient of kinetic friction between the 15 kg block and the plane is 0.25. Find the acceleration of the blocks.
255ms2
079ms2
477ms2
311ms2
14 A 2 kg and a 4 kg hang freely at opposite ends of a light inextensible string which passes over a small and light pulley fixed to a rigid support. Calculate the acceleration of the system.
33ms2
267ms2
441ms2
267ms2
15 Which of the following quantities has the same dimensions as work?
momentum
impulse
moment of a force
pressure
16 Which of the following is not true?
A crate sliding across the floor does work against frictional forces
Work is done if a component a force acting on an object exists in the direction of its displacement
A man with a bag of cement on his head does work to move the bag of cement as he walks from place to place on a flat horizontal floor
Work is a scalar quantity
17 Which of the following properties of a ball is conserved as it falls freely in a vacuum?
kinetic energy
gravitational potential energy
monentum
mechanical energy
18 How much work is done when a bucket of mass 1.5 kg with 10 kg of water in it is pulled up from the bottom of a well 8 m deep? Take g=98ms2
100.3 J
2000.5 J
901.6 J
453.7 J
19 A 65 kg sprinter completes a 100 m race in 9.83 s. Calculate the average kinetic energy of the sprinter
3.36 kJ
2.11 kJ
34.15 kJ
65.42 kJ
20 Which of the following is NOT a unit of energy?
joule
newton-metre
kilowatt-hour
watt
1. The gravitational field strength at a height h above the surface of the Earth can be calculated using the formula: g(R^2)/(R+h)^2, where g is the acceleration due to gravity on the surface of the Earth and R is the radius of the Earth. Therefore, the correct option is gR^2(R+h)^2.
2. The instrument used for experimental determination of the value of the universal gravitational constant G is called the Cavendish balance.
3. The acceleration due to gravity at a certain altitude above the Earth's surface can be calculated using the formula: a = g(R^2)/(R+h)^2, where g is the acceleration due to gravity on the surface of the Earth, R is the radius of the Earth, and h is the altitude above the surface. Rearranging the formula to solve for h gives: h = (a*R^2)/g. Plugging in the given values: a = 49 m/s^2, R = 6410^6 m, and g = 9.8 m/s^2, we can calculate the altitude to be 465106 m.
4. The weight of the man on the moon can be calculated using the formula: weight = (mass on moon * acceleration due to gravity on moon). The acceleration due to gravity on the moon can be calculated using the formula: g = (G * mass of moon) / (radius of moon)^2. Plugging in the given values: mass on moon = 750 N / 9.8 m/s^2, mass of moon = 7.36 * 10^22 kg, radius of moon = 1.74 * 10^6 m, we can calculate the weight to be 200.5 N.
5. The speed of the satellite can be calculated using the formula: speed = sqrt((G * mass of Earth) / (radius of Earth + altitude)) and the period can be calculated using the formula: period = (2 * pi * (radius of Earth + altitude)) / speed. Plugging in the given values: mass of Earth = 5.98 * 10^24 kg, radius of Earth = 6.41 * 10^6 m, altitude = 300 km = 3 * 10^5 m, and G = 6.67 * 10^-11 Nm^2/kg^2, we can calculate the speed to be 497.2 km/s and the period to be 55,105 s.
6. The orbital radius and speed of a synchronous satellite can be calculated using the formula: radius = (G * mass of Earth * period^2 / (4 * pi^2))^(1/3) and speed = 2 * pi * radius / period. Plugging in the given values: mass of Earth = 5.98 * 10^24 kg, period = 24 h = 24 * 60 * 60 s, and G = 6.67 * 10^-11 Nm^2/kg^2, we can calculate the orbital radius to be 42,107 m and the speed to be 3,100 m/s.
7. The escape velocity from the surface of a planet can be calculated using the formula: escape velocity = sqrt(2 * G * mass of planet / radius of planet). Plugging in the given values: mass of Jupiter = 1.9 * 10^27 kg, radius of Jupiter = 7.15 * 10^8 m, and G = 6.67 *10^-11 Nm^2/kg^2, we can calculate the escape velocity to be 59.5 km/s.
8. The tension in the string when the ball is at the top of the circle can be calculated using the formula: tension = mass * (gravity + acceleration). Plugging in the given values: mass = 50 g = 0.05 kg, gravity = 10 m/s^2, and acceleration = -10 m/s^2 (since it is moving upwards), we can calculate the tension to be 70.7 N.
9. The acceleration of the elevator can be calculated using the formula: acceleration = (force - weight) / mass. Plugging in the given values: force = 12,104 N, weight = mass * gravity = 20 * 9.8 N, and mass = 20,103 kg, we can calculate the acceleration to be 38 m/s^2 upward.
10. The frictional force retarding the motion of the box can be calculated using the formula: frictional force = force - (mass * acceleration). Plugging in the given values: force = 40 N, mass = 5 kg, and acceleration = 3 m/s^2, we can calculate the frictional force to be 25 N.
11. The acceleration of the system and the tension in the string can be calculated using the following equations:
acceleration = (m1 * g - m2 * g) / (m1 + m2)
tension = m2 * acceleration + m2 * g
Plugging in the given values: m1 = 2 kg, m2 = 4 kg, g = 9.8 m/s^2, we can calculate the acceleration to be 2.67 m/s^2 and the tension to be 13.3 N.
12. The acceleration of the block can be calculated using the formula: acceleration = (tension - frictional force) / mass. Plugging in the given values: tension = 250 N, frictional force = 8.0 N, and mass = 20 kg, we can calculate the acceleration to be 21 m/s^2.
13. The acceleration of the blocks can be calculated using the formula: acceleration = (m2 * g - m1 * g) / (m1 + m2 - (frictional force / g)), where m1 and m2 are the masses of the blocks, g is the acceleration due to gravity, and frictional force is the force opposing the motion. Plugging in the given values: m1 = 15 kg, m2 = 13 kg, g = 9.8 m/s^2, and frictional force = coefficient of kinetic friction * normal force = 0.25 * m1 * g * cos(theta), where theta is the angle of inclination, we can calculate the acceleration to be 0.79 m/s^2.
14. The acceleration of the system can be calculated using the formula: acceleration = (m2 - m1) * g / (m1 + m2), where m1 and m2 are the masses of the blocks and g is the acceleration due to gravity. Plugging in the given values: m1 = 2 kg, m2 = 4 kg, and g = 9.8 m/s^2, we can calculate the acceleration to be 2.67 m/s^2.
15. The quantity that has the same dimensions as work is energy.
16. The statement that is not true is: A crate sliding across the floor does work against frictional forces.
17. The property that is conserved as a ball falls freely in a vacuum is mechanical energy.
18. The work done when pulling the bucket of mass 1.5 kg with 10 kg of water up from the bottom of a well can be calculated using the formula: work = force * distance. Since the force required to lift the bucket is equal to the weight of the bucket and water, the work done is work = (weight of bucket + weight of water) * distance. Plugging in the given values: weight of bucket = mass of bucket * g, weight of water = mass of water * g, mass of bucket = 1.5 kg, mass of water = 10 kg, g = 9.8 m/s^2, and distance = 8 m, we can calculate the work to be 100.3 J.
19. The average kinetic energy of the sprinter can be calculated using the formula: kinetic energy = (1/2) * mass * velocity^2. Plugging in the given values: mass = 65 kg and velocity = distance / time = 100 m / 9.83 s, we can calculate the average kinetic energy to be 34.15 kJ.
20. The unit that is not a unit of energy is the watt. The watt is a unit of power, not energy.