Variation of G Due to Height and Depth

Q.

State and prove law of conservation of energy in case of freely falling body.

Q. A body weighs $200N$ on the surface of the earth. How much will it weight halfway down to the centre of the earth ?

1. $150N$
2. $200N$
3. $250N$
4. $100N$

Q. The acceleration due to gravity at a height $1km$ above the earth is the same as at a depth $d$ below the surface of earth. Then

1. $d=2km$
2. $d=1km$
3. $d=\frac{3}{2}km$
4. $d=\frac{1}{2}km$

Q. A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$. $F$ is proportional to :

1. $\frac{1}{{ϵ}_0}{\sigma }^2{R}^2$
2. $\frac{1}{{ϵ}_0}{\sigma }^{2}R$
3. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R}$
4. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R^2}$

Q.

Write any three points of difference between G and ‘g ’.

Q. There is no atmosphere on the moon because

1. it is closer to the earth
2. it revolves around the earth
3. the escape velocity of gas molecules is less than their root mean square velocity on the moon
4. the escape velocity of gas molecules is more than their root mean square velocity on the moon

Q. A satellite of mass $m$, revolving in a circular orbit of radius $r$ around the earth of mass $M$ has magnitude of total energy $E$. Then its angular momentum will be

1. $\sqrt{2Emr}$
2. $\sqrt{Em{r}^2}$
3. $\sqrt{4Em{r}^2}$
4. $\sqrt{2Em{r}^2}$

Q. A new system of units is proposed in which unit of mass is a kg unit of lenth $\beta$ m and unit of time y s . How much will 5 J measure in this new system ?

Q.

The acceleration due to gravity becomes $\frac{g}{2}$ at a height equal to ($g$= acceleration due to gravity on the surface of the earth)

1. $4R$

2. $\frac{R}{4}$

3. $2R$

4. $\frac{R}{2}$

Q.

A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

Q.

A coin and a feather are dropped together in a vacuum.

1. The coin will reach the ground first.

2. The feather will reach the ground first.

3. Both the bodies will reach the ground at the same time.

4. The feather will not fall down.

Q.

What is the value of g on the surface of sun?

Mass of sun$=1.99\times {10}^{30}kg$

Radius of sun $=6.96\times {10}^{8}m$

Q.

Weight of a body of mass m decreases by $1\%$ when it is raised to height h above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is

1. 

2. 

3. 

4. 

Q.

The acceleration due to gravity on the earth’s surface at the poles is $g$ and angular velocity of the earth about the axis passing through the pole is $\omega$. An object is weighed at the equator and at a height $h$ above the poles by using a spring balance. If the weights are found to be same, then $h$ is : ($h<<R$, where $R$ is the radius of the earth)

1. $\frac{R^2{\omega }^2}{g}$

2. $\frac{R^2{\omega }^2}{8g}$

3. $\frac{R^2{\omega }^2}{4g}$

4. $\frac{R^2{\omega }^2}{2g}$

Q.

Does the time-period of a pendulum depend on mass of its bob?

Q.

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on ${60}^{\circ }$ latitude becomes zero is (Radius of earth = 6400 At the poles g = 10$m{s}^{-2}$)

1. 

2. 

3. 

4. 

Q. Two masses $A$ and $B$ of $10kg$ and $5kg$ respectively, are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown in figure, the coefficient of friction of $A$ with the table is $0.2$. The minimum mass (in$kg$) of $C$ that may be placed on $A$ to prevent it from moving is:

Q.

A stone is released from an elevator going up with an acceleration a.The acceleration of the stone after the release is ?

Q. The atmosphere on a planet is possible only if
[$v_{rms}$ is root mean square speed of gas molecules on planet and $v_e$ is escape speed on its surface]

1. $v_{rms}=v_e$
   
2. $v_{rms}>v_e$
   
3. $v_{rms}\le v_e$
   
4. $v_{rms}<v_e$
   

Q. Given below are two statements: One is labelled as
Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the centre of earth without any variation in its magnitude.

Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below.

Q.

If polar ice caps melt, then the angular velocity of rotation of earth

1. Becomes zero

2. Remains constant

3. Increases

4. Decreases

Q. A ball rolls off top of a staircase with a horizontal velocity u m/s. If the steps are h metre high and b metre wide, the ball will just hit the edge of nth step if n equals to

1. 
2. 
3. 
4. 

Q. A body freely falling from the rest has a velocity ${}^{\prime }{v}^{\prime }$ after it falls through a height ${}^{\prime }{h}^{\prime }$. The distance it has to fall down for its velocity to become double, is

1. $6h$
2. $4h$
3. $2h$
4. $8h$

Q. A particle is projected with a velocity $u$ making an angel $\theta$ with the horizontal. At any instant its velocity becomes $v$ which is perpendicular to the initial velocity $u$. Then $v$ is

1. $u\cos \theta$
2. $u\sec \theta$
3. $u\cot \theta$
4. $u\tan \theta$

Q.

Classify the following quantities as scalar and vector quantities in a tabular form.

Force, Mass, Temperature, Momentum, Moment of force, Pressure, Displacement, Acceleration, Electric potential, Distance.

Q.

The weight of an object at the center of the earth is zero.

1. True
2. False

Q. The equivalent capacitance of the infinite ladder shown in the figure between points $\text{A}$ & $\text{B}$ will be

1. $2\mu \text{F}$
2. $1\mu \text{F}$
3. $4\mu \text{F}$
4. $\frac{1}{2}\mu \text{F}$

Q. A wheel of mass $10kg$ has a moment of inertia of $160kg{m}^2$ about its own axis. The radius of gyration is

1. $5m$
2. $4m$
3. $6m$
4. $10m$

Q.

Estimate the speed of vertically falling raindrops from the following data. Radius of the drops = 0.02 cm, viscosity of air = $1.8\times {10}^{-4}$ poise, g = $9.9\times 10m{s}^{-2}$ and density of water = $1000kg{m}^{-3}$

Q.

Weighing machine measure what mass or weight of human body?