Answer:
0.087 m
Explanation:
Length of the rod, L = 1.5 m
Let the mass of the rod is m and d is the distance between the pivot point and the centre of mass.
time period, T = 3 s
the formula for the time period of the pendulum is given by
.... (1)
where, I is the moment of inertia of the rod about the pivot point and g is the acceleration due to gravity.
Moment of inertia of the rod about the centre of mass, Ic = mL²/12
By using the parallel axis theorem, the moment of inertia of the rod about the pivot is
I = Ic + md²

Substituting the values in equation (1)


12d² -26.84 d + 2.25 = 0


d = 2.15 m , 0.087 m
d cannot be more than L/2, so the value of d is 0.087 m.
Thus, the distance between the pivot and the centre of mass of the rod is 0.087 m.
Answer:
2.10L
Explanation:
Given data
V1= 2.5L
T1= 275K
P1= 2.1atm
P2= 2.7 atm
T2= 298K
V2= ???
Let us apply the gas equation
P1V1/T1= P2V2/T2
substitute into the expression we have
2.1*2.5/275= 2.7*V2/298
5.25/275= 2.7*V2/298
Cross multiply
275*2.7V2= 298*5.25
742.5V2= 1564.5
V2= 1564.5/742.5
V2= 2.10L
Hence the final volume is 2.10L
Answer:
19.01 N
Explanation:
F = Force being applied to the crate = 45 N
= Angle at which the force is being applied = 
Horizontal component of force is given by

The horizontal component of the force acting on the crate is 19.01 N.