A 4.0 kg mass is released from rest at the top of a frictionless ramp 2.0 m above ground. It slides down the ramp to a level, horizontal portion of frictionless track and then collides with a stationary 8.0 kg mass. Immediately after the collision, the larger mass has a velocity v_l = +3.5 m/s (i. e., heading to the right).
The velocity v_s of the smaller mass just after the collision:

A) -0.74 m/s B) +0.74 m/s C) -2.6 m/s D) +2.6 m/s E) 0 m/s

(A)−0.74m/s

Explanation:

We are given that

Mass ,=4 kg

Distance, d=2 m

We have to find the velocity of smaller mass just after the collision.

Initial velocity of smaller mass,u=0

Velocity of smaller mass at the bottom

According to law of conservation of momentum

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.