5. a pendulum consisting of a mass m = 0.2 kg attached to a massless rod of length l = 0.3 m is pulled to an angle θ = 15° and released. the speed of the mass at the bottom of the swing is

a) 0.742 m/s

b) 1.03 m/s

c) 0.254 m/s

d) 0.448 m/s

e) 0.595 m/s

option D

Explanation:

given,

mass of pendulum = 0.2 Kg

length of rod = 0.3 m

angle of inclination = 15°

speed of mass at bottom = ?

using conservation of energy  

PE is converted into kinetic energy

h = L - L cos θ

h = 0.3 - 0.3 cos 15°

h = 0.0102 m

now,

    v = √0.2

   v = 0.448

hence, the correct answer is option D

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂