Leaky sandbag A bag of sand originally weighing 144 lb was lifted at a constant rate. As it rose, sand also leaked out at a constant rate. The sand was half gone by the time the bag had been lifted to 18 ft. How much work was done lifting the sand this far? (Neglect the weight of the bag and lifting equipment.)

Explanation:

Let m be the total mass initially and h be the height up-to which it is lifted.

Rate of fall of sand

= m/(2xh) lb/ft

At any height p , mass leaked out = m/(2xh) x p

At certain height p, mass  will  be m - m/(2xh) x p . This mass is lifted by small distance dp

work done

dW = [m - m/(2xh) x p ] g dp

Integrating it from 0 to h , we get the total value of work done

W = ∫[m - m/(2xh) x p ] g dp

= mg ( p - 1 / 2h x p²/2 )

Now taking limit between 0 to h

W = mg ( h - 1/2h x h²/2)

= mg ( h - h / 4 )

3 / 4 x mgh

= .75 x 144 x 32 x 18

= 62208 ft-poundal .

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.