Advertisements
Advertisements
प्रश्न
The gravitational force acting on a particle of 1 g due to a similar particle is equal to 6.67 × 10−17 N. Calculate the separation between the particles.
Advertisements
उत्तर
Mass of the particle, m = 1 gm \[= \frac{1}{1000} kg\]
Let the distance between the two particles be r.
Gravitational force between the particle, F = 6.67 × 10−17 N
Also, \[F = \frac{\text{ G m} _1 \text{ m }_2}{r^2}\]
Substituting the respective values in the above formula, we get :
\[6 . 67 \times {10}^{- 17} = \frac{6 . 67 \times {10}^{- 11} \times \left( 1/1000 \right) \times \left( 1/1000 \right)}{r^2}\]
\[ \Rightarrow r^2 = \frac{6 . 67 \times {10}^{- 6} \times {10}^{- 11}}{6 . 67 \times {10}^{- 17}}\]
\[ = \frac{{10}^{- 17}}{{10}^{- 17}} = 1\]
\[ \Rightarrow r = \sqrt{1} = 1 \text{ m }\]
∴ The separation between the particles is 1 m.
APPEARS IN
संबंधित प्रश्न
State if the following statement is true or false. Give a reason for your answer.
Work done in the motion of a body over a closed loop is zero for every force in nature.
A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by
`F = -hati+2hatj+3hatkN`
Where `hati,hatj,hatk` are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?
A boy is sitting on a chair placed on the floor of a room. Write as many action-reaction pairs of forces as you can.
List all the forces acting on the block B in figure.
A satellite is projected vertically upwards from an earth station. At what height above the earth's surface will the force on the satellite due to the earth be reduced to half its value at the earth station? (Radius of the earth is 6400 km.)
The work done by the external forces on a system equals the change in
A block of mass m slides down a smooth vertical circular track. During the motion, the block is in
A constant force of 2⋅5 N accelerates a stationary particle of mass 15 g through a displacement of 2⋅5 m. Find the work done and the average power delivered.
A particle moves from a point \[\overrightarrow{r}_1 = \left( 2 m \right) \overrightarrow{ i } + \left( 3 m \right) \overrightarrow{ j } \] to another point
\[\overrightarrow{r}_2 = \left( 3 m \right) \overrightarrow{ i } + \left( 2 m \right) \overrightarrow{ j } \] acts on it. Find the work done by the force on the particle during the displacement.
A block of mass 2 kg kept at rest on an inclined plane of inclination 37° is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for one second. Find the work done by the force of gravity in that one second if the work done by the applied force is 40 J.
The 200 m free-style women's swimming gold medal at Seoul Olympics in 1988 was won by Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and 57⋅56 seconds. Assume that she covered most of the distance with a uniform speed and had to exert 460 W to maintain her speed. Calculate the average force of resistance offered by the water during the swim.
In a children's park, there is a slide which has a total length of 10 m and a height of 8⋅0 m . A vertical ladder is provided to reach the top. A boy weighing 200 N climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the slide is three tenth of his weight. Find (a) the work done by the ladder on the boy as he goes up; (b) the work done by the slide on the boy as he comes down. Neglect any work done by forces inside the body of the boy
A lawn roller is pulled along a horizontal surface through a distance of 20 m by a rope with a force of 200 N. If the rope makes an angle of 60° with the vertical while pulling, the amount of work done by the pulling force is:
A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is ______.
A graph of potential energy V(x) verses x is shown in figure. A particle of energy E0 is executing motion in it. Draw graph of velocity and kinetic energy versus x for one complete cycle AFA.
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 30° by a force of 10 N parallel to the inclined surface (Figure). The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, calulate
- work done against gravity
- work done against force of friction
- increase in potential energy
- increase in kinetic energy
- work done by applied force.
A block of mass m is taken from A to B slowly under the action of a constant force R Work done by this force is ______.
If a force varies linearly with displacement, the area under the F-s graph forms:
What does 'dW' represent in the variable force work calculation?
