Two wheels have the same mass and radius of 4.2 kg and 0.42 m, respectively. One has (a) the shape of a hoop and the other (b) the shape of a solid disk. The wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. Each turns through an angle of 14 rad in 8.3 s. Find the net external torque that acts on each wheel.

τsolid = 0.15 N•m

τhoop = 0.30 N•m

Explanation:

θ = ½αt²

α = 2θ/t² = 2(14)/8.3² = 0.406445 rad/s²

Solid disk I = ½mr² = ½(4.2)0.42² = 0.37044 kg•m²

τ = Iα = 0.37044(0.406445) = 0.150563... N•m

Hoop disk I = mr² = (4.2)0.42² = 0.74088 kg•m²

τ = Iα = 0.74088(0.406445) = 0.301127... N•m

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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.