A raindrop initially has mass M_0 = 0.277~\mathrm{g}M 0 =0.277 g and, due to gravity, starts falling from rest through a cloud. One way to model the growth of a raindrop is to assume that its mass grows proportionally to the product of its instantaneous mass and velocity, according to the following equation \dfrac{dM}{dt} = kMV. dt dM =kMV. Here, kk is a constant of proportionality, which we take to be k = 6.99~\mathrm{m}^{-1}.k=6.99 m −1 . What is the speed of the rain drop when its mass has doubled its initial value?

Aman tries to push a box of mass 4 kg with a force of 5 n but the box remains stationary if the coefficient of static friction is 0.45, what is the value of the maximum force of friction?

The density of a liquid could be found by using

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?