The range of gravitational forces is:
infinity
\( 10^{-2} \) m
Step 1: Understanding the Range of Gravitational Force Gravitational force is a fundamental force of nature that acts between any two masses. Unlike other fundamental forces (such as weak nuclear force or strong nuclear force), gravity: - Has an infinite range. - Gets weaker with increasing distance but never fully disappears.
Step 2: Explanation The gravitational force between two masses \( m_1 \) and \( m_2 \) is given by Newton's Law of Universal Gravitation: \[ F = G \frac{m_1 m_2}{r^2} \] where \( G \) is the gravitational constant and \( r \) is the distance between the two masses. As \( r \) increases, \( F \) decreases, but it never becomes exactly zero. This indicates that gravitational force has an infinite range.
Thus, the correct answer is: \[ \text{infinity} \]
The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \( R = 2 \, \text{m} \). Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the side view mirror is \( a \). The value of \( 100a \) is _____________ m/s\(^2\).
In a simple pendulum experiment for the determination of acceleration due to gravity, the error in the measurement of the length of the pendulum is 1% and the error in the measurement of the time period is 2%. The error in the estimation of acceleration due to gravity is:
Find \( \frac{dy}{dx} \) for the given function:
\[ y = \tan^{-1} \left( \frac{\sin^3(2x) - 3x^2 \sin(2x)}{3x \sin(2x) - x^3} \right). \]
The length of the normal drawn at \( t = \frac{\pi}{4} \) on the curve \( x = 2(\cos 2t + t \sin 2t) \), \( y = 4(\sin 2t + t \cos 2t) \) is:
If water is poured into a cylindrical tank of radius 3.5 ft at the rate of 1 cubic ft/min, then the rate at which the level of the water in the tank increases (in ft/min) is:
The function \( y = 2x^3 - 8x^2 + 10x - 4 \) is defined on \([1,2]\). If the tangent drawn at a point \( (a,b) \) on the graph of this function is parallel to the X-axis and \( a \in (1,2) \), then \( a = \) ?