Advertisements
Advertisements
प्रश्न
The gravitational field in a region is given by \[E = \left( 2 \overrightarrow{i} + 3 \overrightarrow{j} \right) N {kg}^{- 1}\] . Show that no work is done by the gravitational field when a particle is moved on the line 3y + 2x = 5.
[Hint : If a line y = mx + c makes angle θ with the X-axis, m = tan θ.]
Advertisements
उत्तर
The gravitational field in a region is given by \[\overrightarrow{E} = 2 \hat i + 3 \hat j\]
Slope of the electric field, \[m_1 = \tan \theta_1 = \frac{3}{2}\]
The given line is 3y + 2x = 5.
Slope of the line, \[m_2 = \tan \theta_2 = - \frac{2}{3}\]
We can see that m1m2 = −1
Since the directions of the field and the displacement are perpendicular to earth other, no work is done by the gravitational field when a particle is moved on the given line.
APPEARS IN
संबंधित प्रश्न
What is the importance of the universal law of gravitation?
The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) (i) a, (ii) b, (iii) c, (iv) 0.
State Kepler’s law which is represented by the relation r3 ∝ T2.
Three equal masses m are placed at the three corners of an equilateral triangle of side a. Find the force exerted by this system on another particle of mass m placed at (a) the mid-point of a side, (b) at the centre of the triangle.
Multiple Choice Question. Select the correct option.
The mass of earth is 6 × 1024 kg and radius of earth is 6.4 × 106 m. The magnitude of force between the mass of 1 kg and the earth is:
Where will you weigh more: at the moon's surface or at the earth's surface?
What is meant by the equation :
`g= Gxxm/r^2`
where the symbols have their usual meanings.
What does a force do in the following case?
You apply brakes to a running car.
Answer the following question.
What are the dimensions of the universal gravitational constant?
The value of universal gravitational constant (G) in the SI unit is ______.
The ______ force is much weaker than other forces in nature.
Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is
The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
Answer the following questions in reference to the figure below:
- Which relation is shown in the figure?
- What will happen if the mass of one of the objects is doubled?
If the mass of one object is doubled and distance remains the same, the gravitational force will ______.
The Superposition Principle states that the net gravitational force on an object is ______.
If the distance between two objects is doubled, the gravitational force becomes ______.
A hollow spherical shell of uniform density exerts what gravitational force on a point mass placed inside it?
