All questions of Potential Energy for Grade 8 Exam

C. 10 kg

G on moon is 1/6 of that of earth.So weight becomes 48/6=8

To find the mass of a body, we can use the formula:

Weight = mass × acceleration due to gravity (g)

Given that the weight of the body is 59 N and the acceleration due to gravity is 9.8 m/s^2, we can rearrange the formula to solve for mass:

mass = weight / acceleration due to gravity

Substituting the given values:

mass = 59 N / 9.8 m/s^2

Calculating this equation gives us:

mass ≈ 6 kg

Therefore, the mass of the body is approximately 6 kg.

Explanation:
- Weight is the force exerted by a body due to gravity, and it is measured in Newtons (N).
- The acceleration due to gravity, denoted by 'g', is the acceleration an object experiences due to the gravitational force. On Earth, the average value of g is approximately 9.8 m/s^2.
- The formula weight = mass × acceleration due to gravity relates weight, mass, and acceleration due to gravity.
- To find the mass, we rearrange the formula and divide both sides by acceleration due to gravity.
- By substituting the given values of weight (59 N) and acceleration due to gravity (9.8 m/s^2) into the formula, we can calculate the mass.
- The final result is approximately 6 kg.

Gravity of earth is 9.8 N acceleration due to gravity is also 9.8 N gravitational force is nothing but the force applied by earth Therefore, f = m*a f,= 10*9.8 f= 98 N

Force of gravitation is inversely proportional to square of distance 1/r^2

Earth is not a perfect sphere. Its radius at equator is greater than poles. Acceleration due to gravity is inversely proportional to the square of its radius. So, the acceleration due to gravity is greatest at poles. Hence, from relation, W = mg, it is clear that weight is highest at the poles.

In combination, the equatorial bulge and the effects of the surface centrifugal force due to rotation mean that sea-level effective gravity increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles, so an object will weigh about 0.5% more at the poles than at the Equator.

Explanation:
When an object is dropped from a height, it falls freely under the influence of gravity. The acceleration due to gravity is approximately 9.8 m/s^2. So, as the stone falls, its speed increases due to the acceleration.

Using the kinematic equation:
We can use the kinematic equation to calculate the final speed of the stone after it has fallen 100 m. The equation is:

v^2 = u^2 + 2as

Where:
v = final velocity (unknown)
u = initial velocity (0 m/s, as the stone is dropped)
a = acceleration due to gravity (9.8 m/s^2)
s = displacement (100 m)

Substituting the given values:
v^2 = 0^2 + 2 * 9.8 * 100
v^2 = 0 + 1960
v^2 = 1960

Taking the square root of both sides:
v = √1960
v ≈ 44.2 m/s

Therefore, the speed of the stone after it has fallen 100 m is approximately 44.2 m/s. So, option B is the correct answer.

Mercury is a non metal... in the question it is asked abt metal....

The apparent loss in weight of an object when it is immersed in a fluid is equal to the weight of the fluid displaced by the object. In this case, the four balls A, B, C, and D displace different volumes of liquid alpha when immersed completely. We need to determine which ball will undergo the maximum apparent loss in weight.

Let's analyze the volume of liquid displaced by each ball:

- Ball A displaces 10 mL of liquid alpha
- Ball B displaces 24 mL of liquid alpha
- Ball C displaces 15 mL of liquid alpha
- Ball D displaces 12 mL of liquid alpha

To determine the maximum apparent loss in weight, we need to find the ball that displaces the greatest volume of liquid alpha.

Comparing the volumes displaced, we can see that:

- Ball B displaces the greatest volume of liquid alpha (24 mL)
- Ball A displaces a smaller volume of liquid alpha (10 mL)
- Ball C displaces a smaller volume of liquid alpha (15 mL)
- Ball D displaces the smallest volume of liquid alpha (12 mL)

Therefore, the ball that will undergo the maximum apparent loss in weight is Ball B.

To find the speed of the ball at the end of 2 seconds, we can use the equation of motion for an object in free fall. The equation is given by:

v = u + gt

Where:
v = final velocity
u = initial velocity (which is 0 in this case as the ball is dropped)
g = acceleration due to gravity (which is approximately 9.8 m/s²)
t = time taken

Let's apply this equation to the given problem:

1. Determine the values:
u = 0 (as the ball is dropped)
g = 9.8 m/s² (acceleration due to gravity)
t = 2 seconds

2. Substitute the values into the equation:
v = 0 + (9.8 m/s²) * (2 seconds)

3. Calculate the result:
v = 0 + (9.8 m/s²) * (2 seconds)
v = 0 + 19.6 m/s

So, the speed of the ball at the end of 2 seconds is 19.6 m/s.

Therefore, the correct answer is option 'B' - 19.6 m/s.

Gravitational force is the force of attraction between two objects with mass. It is given by the equation:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force,
G is the gravitational constant (6.67 × 10^(-11) N m^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.

Given:
m1 = 200 kg
m2 = 800 kg
r = 50 m

Substituting the given values into the equation, we have:

F = (6.67 × 10^(-11) N m^2/kg^2) * (200 kg * 800 kg) / (50 m)^2

Simplifying the expression:

F = (6.67 × 10^(-11) N m^2/kg^2) * (160,000 kg^2) / (2500 m^2)

F = (6.67 × 10^(-11) N m^2/kg^2) * 64

F = 4.2688 × 10^(-9) N

Rounding off to the correct number of significant figures, we get:

F = 4.26 × 10^(-9) N

Therefore, the gravitational force between the two objects is 4.26 × 10^(-9) N.

Explanation:

When a rectangular block is placed on the ground, the pressure exerted by the block on the ground depends on the area of contact between the block and the ground. This pressure is given by the formula:

Pressure = Force/Area

In this case, the force is the weight of the block and the area of contact is determined by the dimensions of the block that are in contact with the ground.

The different ways the block can be placed on the ground are:

1. Length and breadth from the base: In this case, the length and breadth of the block are in contact with the ground. The area of contact is given by the product of the length and breadth of the block.

2. Length and height from the base: In this case, the length and height of the block are in contact with the ground. The area of contact is given by the product of the length and height of the block.

3. Breadth and height from the base: In this case, the breadth and height of the block are in contact with the ground. The area of contact is given by the product of the breadth and height of the block.

Comparing the areas of contact:

To determine which placement exerts the maximum pressure on the ground, we need to compare the areas of contact in each case.

- Area of contact in the first case (length and breadth from the base): Length * Breadth
- Area of contact in the second case (length and height from the base): Length * Height
- Area of contact in the third case (breadth and height from the base): Breadth * Height

Comparison:

Since the length, breadth, and height of the block are given as 50 cm, 25 cm, and 10 cm respectively, we can compare the areas of contact in each case.

- Area of contact in the first case: 50 cm * 25 cm = 1250 cm^2
- Area of contact in the second case: 50 cm * 10 cm = 500 cm^2
- Area of contact in the third case: 25 cm * 10 cm = 250 cm^2

Conclusion:

From the comparison, we can see that the area of contact is maximum in the first case (length and breadth from the base). Therefore, the maximum pressure is exerted when the length and breadth of the block are in contact with the ground. Therefore, the correct statement is option 'A': The maximum pressure is exerted when the length and breadth from the base.

Explanation:

Weight of the object in air:
- The weight of the object in air is 10 N.

Weight of the object in liquid:
- When the object is fully immersed in a liquid, it weighs 8 N.
- The loss in weight of the object when immersed in the liquid is due to the buoyant force acting on it.

Weight of the liquid displaced:
- The weight of the liquid displaced by the object is equal to the difference in weight of the object in air and in liquid.
- Weight of the displaced liquid = Weight of the object in air - Weight of the object in liquid
- Weight of the displaced liquid = 10 N - 8 N
- Weight of the displaced liquid = 2 N

Therefore, the weight of the liquid displaced by the object is 2 N.

The value of 'g' that is gravity is greater at the poles because the gravitational pull is maximum at the poles and decreases as it comes down toward the equator.

W = mg
mg = W
m=W÷g
m = 59÷9.8
m = 6.02 or 6 ( Approx )

To find the initial velocity of the ball, we can use the equation of motion for vertical motion:

h = ut + (1/2)gt^2

where:
h = height or distance traveled by the ball (19.6 m in this case)
u = initial velocity of the ball (what we need to find)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken by the ball to reach the maximum height (which is the same as the time taken for the ball to come back down)

Here, the ball is thrown vertically upwards, which means that its final velocity at the maximum height will be zero. The time taken to reach the maximum height can be found using the equation:

v = u + gt

Since the final velocity is zero, we have:
0 = u + (-9.8)t
u = 9.8t

Now, substituting this value of u in the equation for height:
h = (9.8t)t + (1/2)(-9.8)t^2
19.6 = 4.9t^2
t^2 = 19.6/4.9
t^2 = 4
t = 2 seconds

Now, substituting the value of t in the equation for u:
u = 9.8t
u = 9.8 * 2
u = 19.6 m/s

Therefore, the initial velocity of the ball is 19.6 m/s, which matches with option B.

Explanation:

When an object is thrown up, it experiences the force of gravity acting on it. The force of gravity is always directed towards the center of the Earth. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the force of gravity on the object is opposite to the direction of its motion.

Force of gravity:
The force of gravity is a force that attracts objects towards each other. On Earth, the force of gravity is due to the mass of the Earth pulling objects towards its center. The magnitude of the force of gravity depends on the mass of the object and the distance between the object and the center of the Earth.

Direction of motion:
When an object is thrown up, it moves in the upward direction initially. As it moves upward, the force of gravity acts in the opposite direction, pulling the object downwards. This force of gravity gradually decreases the upward velocity of the object until it reaches its highest point and comes to a momentary stop.

Zero force at the highest point:
At the highest point of its trajectory, the object momentarily stops moving in the upward direction and starts moving in the downward direction. At this point, the force of gravity becomes zero because there is no further upward motion for the force to oppose.

Increasing force as it rises up:
The force of gravity on an object is constant regardless of its position or motion. However, the effect of gravity on the object changes as it rises up. Initially, when the object is close to the surface of the Earth, the force of gravity is stronger, and as the object moves higher, the force of gravity decreases due to the increase in distance from the center of the Earth.

Therefore, the correct answer is option 'A' - the force of gravity is opposite to the direction of motion when an object is thrown up.

Weight on the Moon

To calculate the weight of a person on the moon, we need to understand the concept of weight and the gravitational force.

Weight and Gravitational Force

Weight is the force with which an object is attracted towards the center of the Earth or any other celestial body. It is directly proportional to the mass of an object. The gravitational force is the force of attraction between two objects due to their masses.

Formula to Calculate Weight

The formula to calculate weight is given by:
Weight = mass * gravitational acceleration

Gravitational Acceleration on the Moon

The gravitational acceleration on the moon is approximately 1/6th of the gravitational acceleration on Earth. The gravitational acceleration on Earth is approximately 9.8 m/s².

Calculation

Given:
Mass of the man = 120 kg
Gravitational acceleration on the moon = 1/6 * 9.8 m/s² = 1.63 m/s²

Using the formula for weight, we can calculate the weight of the man on the moon:

Weight = mass * gravitational acceleration
Weight = 120 kg * 1.63 m/s²
Weight = 195.6 N

Rounding off the weight to the nearest whole number, the man would weigh approximately 196 N on the moon.

Conclusion

Therefore, the correct answer is option 'B' - 196 N. The weight of the man on the moon is approximately 196 Newtons.

To find the value of acceleration due to gravity on the surface of the moon, we can use the formula for gravitational acceleration:

g = G * (M / R^2)

where:
g is the acceleration due to gravity
G is the universal gravitational constant (6.7 × 10^–11 Nm^2/kg^2)
M is the mass of the moon (7.4 × 10^22 kg)
R is the radius of the moon (1740 km = 1.74 × 10^6 m)

Let's substitute the given values into the formula and calculate the acceleration due to gravity:

g = (6.7 × 10^–11 Nm^2/kg^2) * (7.4 × 10^22 kg) / (1.74 × 10^6 m)^2

Calculating this expression:

g = (6.7 × 7.4 × 10^11 × 10^22) / (1.74 × 1.74 × 10^12)

Simplifying the expression:

g = (49.58 × 10^33) / (3.0276 × 10^12)

g ≈ 16.35 m/s^2

Therefore, the value of acceleration due to gravity on the surface of the moon is approximately 16.35 m/s^2.

So, the correct answer is option C) 1.63 m/s^2.

The force of gravitation between two bodies in the universe does not depend on the total of their masses. This can be explained by understanding the basic principles of Newton's law of universal gravitation.

Newton's law of universal gravitation states that the force of gravitation between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it can be expressed as:

F = G * (m1 * m2) / r^2

where F is the force of gravitation, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between their centers.

Based on this equation, we can analyze each option:

a) The distance between them: According to Newton's law of universal gravitation, the force of gravitation is inversely proportional to the square of the distance between the bodies. As the distance increases, the force of gravitation decreases, and vice versa. Therefore, the force of gravitation does depend on the distance between the bodies.

b) Product of their masses: As shown in the equation, the force of gravitation is directly proportional to the product of the masses of the two bodies. If either of the masses is increased, the force of gravitation will increase, and vice versa. Therefore, the force of gravitation does depend on the product of their masses.

c) The total of their masses: The total of their masses refers to the sum of the masses of the two bodies. However, the equation for the force of gravitation does not include the sum of the masses. It only considers the product of the masses. Therefore, the force of gravitation does not depend on the total of their masses.

d) The gravitational constant: The gravitational constant, denoted by G, is a fundamental constant in physics. It is a fixed value that determines the strength of the gravitational force. While the gravitational constant is essential for calculating the force of gravitation, it does not affect the dependence of the force on the masses or distance between the bodies.

In conclusion, the force of gravitation between two bodies in the universe depends on the distance between them (option a) and the product of their masses (option b), but it does not depend on the total of their masses (option c) or the gravitational constant (option d).