Equation of Motion of Free Fall

Q. When a ball is thrown vertically upwards, it goes through a distance of 19.6 m. Find the initial velocity of the ball and the time taken by it to rise to the highest point. (Acceleration due to gravity, $g=9.8m{s}^{-2}$) [3 MARKS]

Q.

The moons radius is $\frac{1}{4}$that of earth and its mass is$\frac{1}{80}$ times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

1. $\frac{g}{4}$

2. $\frac{g}{5}$

3. $\frac{g}{6}$

4. $\frac{g}{8}$

Q.

The initial velocity $v_1$ required to project a body vertically upward from the surface of the earth to just reach a height of $10R$, where$R$ is the radius of the earth, may be described in terms of escape velocity$v_e$ such that $v_i=\sqrt{\left(\frac{x}{y}\right)}{v}_e$. The value of x will be_______.

Q. What will be the sign of accelertation due to gravity on a body near earth, when it is thrown vertically upwards? Take the upward direction as positive.

1. Positive
2. Negative
3. Negligible
4. Zero

Q.

A child is swinging a swing minimum and the maximum heights of swing from the Earths surface are $0.75mand2m$ respectively. What will be the maximum velocity of this swing?

Q.

If a ball is thrown vertically upwards with a velocity of 40$\frac{m}{s}$, assuming $(g=10\frac{m}{s^2})$ then what will be the velocity of the ball after two seconds?

1. 15 m/s

2. 28 m/s

3. 25 m/s

4. 20 m/s

Q.

Calculate the value of $g$ on the surface of earth.

Q.

A stone piece is just dropped from a height of $180m$. If its velocity increases uniformly at the rate of $10m/s^2$, with what velocity will it strike the ground? How much time does the stone take to reach the ground?

Q. ntA body is projected vertically upwards with speed 10m/s and other at same time with same speed in downward direction from the top of a tower .The magnitude of acceleration of first body with respect to second is( g=10m/s)n

Q. The value of acceleration due to gravity at the surface of all planets is the same.

1. True
2. False

Q.

Name the factors on which the g of a planet depends.How?

Q. What will be the speed of a ball at it's maximum height when it is thrown vertically upwards with a speed of 9.8 m/s?

1. Zero
2. $9.8m{s}^{-1}$
3. $10m{s}^{-1}$
4. $1m{s}^{-1}$

Q.

Calculate the acceleration due to gravity on the surface of the moon if the mass of the moon is $7.36\times {10}^{22}kg$and the radius is$1740km$. What will be the weight of a body of mass $10kg$ on the moon? Assume the value of $G$ $\left(G=6.67\times {10}^{-11}\frac{N{m}^2}{kg}\right)$.

Q.

Consider the following statements:
A. The acceleration due to gravity on the Moon is equal to that of the Earth.
B. The value of G is independent of the nature, size and mass of the interacting bodies.
Which of these statement(s) is/are correct?

1. A only
2. B only
3. Both A and B
4. Neither A nor B

Q. A ball falls off a table and reaches the ground in $1s$. Assuming $g=10m{s}^{-2}$. Calculate its speed on reaching the ground and the height of the table.

1. $5m{s}^{-1}$ and $5m$
2. $20m{s}^{-1}$ and $10m$
3. $10m{s}^{-1}$ and $5m$
4. $30m{s}^{-1}$ and $15m$

Q.

A heavy object and a lighter object are allowed to fall from the certain height in the absence of air then how acceleration and velocity varies?

Q. At what altitude (h) above the earths surface would the acceleration due to gravity be one fourth of its value at the earths surface

Q. The height which the acceleration due to gravity is reduced to one fourth of the gravity on the surface of the Earth is

Q. Acceleration due to gravity $g$ near the surface of a planet of mass $M$ and radius $R$ is given by:
$G$ is the Universal constant.

1. $g=\frac{GM}{R}$
2. $g=\frac{GR}{M^2}$
3. $g=\frac{G{M}^2}{R}$
4. $g=\frac{GM}{R^2}$

Q. Pick out the correct relation(s) between universal gravitational constant $\left(G\right)$ and acceleration due to gravity $\left(g\right)$
M = mass of earth,
R = radius of earth.

1. $g=\frac{GM}{R^2}$
2. $g=\frac{R^2}{GM}$
3. $G=\frac{g{R}^2}{M}$
4. $G=\frac{M}{g{R}^2}$

Q. What is the greatest height to which it will rise if a body is thrown vertically upward with a velocity of V

Q. What is free fall

Q.

A body weighs $1kg$on the surface of the Moon. If the mass of the Moon is $7.4\times {10}^{22}kg$, the radius of the Moon is $1740km$ and the gravitational constant is $6.7\times {10}^{-11}N{m}^2/k{g}^2$, calculate the acceleration produced in the Moon?

Q.

Name the acceleration produced in a body falling freely in a vacuum.

Q. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) the maximum height to which it rises.
(ii) the total time it takes to return to the surface of the earth.
[5 Marks]
[Free fall]

Q. Consider two planets with equal masses having radius $r_1$ and $r_2$ such that $r_1>r_2$. The force of gravities at their surfaces are $F_1$ and $F_2$ respectively for a mass $m$. Which of the following conditions are true?

1. $F_1>F_2$
2. $F_1<F_2$
3. $F_1=F_2$
4. $F_1\le F_2$

Q. A ball thrown up vertically returns to the thrower after $6s$. Find the position of the ball after $4s$.
(Take acceleration due to gravity as $9.8m{s}^{-2}$)

1. $39.2m$
2. $41.2m$
3. $29.2m$
4. $44.4m$

Q. A passenger in a moving train tosses a coin which falls behind him. It means that the motion of the train is

1. Uniform
2. Retarded
3. Along circular tracks
4. Accelerated

Q.

Derive the relationship between $g$‘ and ’$G$ .

Q. The acceleration due to gravity at three places $\text{A},\text{B},$ and $\text{C}$ on Earth are given by $9.8\text{m}{\text{s}}^{-2},9.81\text{m}{\text{s}}^{-2}$ and $9.78\text{m}{\text{s}}^{-2}$ respectively. Which of the following statements is true?

1. $\text{B}$ is the nearer to the centre of the Earth than the other two.
2. All of the above.
3. The order of the strength of the Earth's gravity is $\text{B}>\text{A}>\text{C}$.
4. $\text{C}$ is the farther from the centre of the Earth than the other two.