1. acc directly proportional to displacement . dir of acc is opp to the displacement.
b1i) w = 3.9 x 103 rads-1
i2) a = 3.2 x 103 ms-2
ii)plot the values a = 3.2x 10-3 and x = -0.21 mm , straight line with negative gradient and passing origin.
c) If it is , cone will resonate when driving freq is close to nat freq , causing damage to the cone.
2. ai) R= 1.8 ohm aii) number = 361 iii) 3000 turns per m
b) force per meter of 1 Nm-1 acting on conductor carrying a current of 1 A placed perpendicular to the field.
ii) B = 9.42 x 10-3 T
c) i) 3.46 x 107 ms-1 ii) 2.0 x 107ms-1
d) magnetic force acting perpendicular to velocity. Hence this force provides the centripetal force . Equate magnetic force = centripetal force
the formula can be shown.
e) The radius r= 0.012 ( taking the vertical component of v)
It will hit the sides of the wall as the diameter of the circle is 2.4 cm which is larger than the radius of th solenoid of 1.4 cm .
3. p= 2.8 x10-14 Ns, b) V = 26.1 V
4a) The number of nuclei is incorrect as the radioactive nuclei is reducing in number . The number of nuclei does not reduce as daughter nuclei is the product of the decay. Hence the nuclei number is the same.
b) Use decay constant = A/N , where N = m /60u. The unit of m must be changed to kg.
The half life = 0.693/decay constant.
half life= 5.27 yrs.
