Arope with length l and mass density l(kg/m) is held in a pile, and you grab an end that sticks up a tiny bit. the pile is then released, and falls downward. as a function of time, what force must your hand apply to the top of the rope to keep it motionless? assume there is no friction of the rope with itself, so the pile is always in freefall.

F=  l  x ( L -  1/2 g t²) g

Explanation:

Given that

length =L m

mass density = l kg/m

Distance cover by time t

y = 1/2 g t²

The remaining length of the pile = L -  1/2 g t²

So the total weight of the remaining length of the pile ,m

m=  l  x ( L -  1/2 g t²)

The force apply to the top of the rope to keep it motionless is F

F= m g

F=  l  x ( L -  1/2 g t²) g

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.