Answer:
Option (b)
Explanation:
let the weight of boat is W. In equilibrium condition, the weight of boat is equal to the buoyant force acting on the boat.
The buoyant force acting on the boat is equal to the weight of water displaced by the boat.
In case of fresh water:
Weight of the boat = weight of fresh water displaced by the boat
W = Volume of fresh water displaced x density of fresh water x g
W = V x 1 x g
W = V x g ....... (1)
In case of salt water:
Let the volume of salt water displaced is V'.
Weight of the boat = weight of salt water displaced by the boat
W = Volume of salt water displaced x density of salt water x g
W = V' x 1.02 x g ..... (2)
Equate equation (1) and equation (2), we get
V x g = V' x 1.02 x g
V' = 0.98 V
Thus, option (b) is true.
Answer:
1.42 seconds
Explanation:
T=2*pi*(sqrt length over gravity)
T=2*pi*(sqrt 0.5/9.8)
T=1.4189
Round to 3 significant digits
T=1.42 seconds
Answer:
The velocity of the ball when its hit the ground will be 54.22 m/sec
Explanation:
We have given height from which ball is dropped h = 150 m
Acceleration due to gravity 
As the ball is dropped so initial velocity will be zero so u = 0 m/sec
According to third equation of motion we know that 


So the velocity of the ball when its hit the ground will be 54.22 m/sec
Answer:
The running horizontal speed should be larger than 1.29 m/s.
Explanation:
In order for the swimmer to just miss the bone-breaking ledge, her horizontal speed must be

in which we need to know how long we she be diving through the air. To determine that, recall the formula for the distance made by an object with acceleration (in this case it is the gravitational acceleration) with no initial (vertical) velocity:

from which it follows that (for non-negative t)

This result can be used in the initial inequality:

The diving lady better gets a speed larger than 1.29 m/s to avoid landing on the ledge.
Answer:
(a) The density of the object is 316/343 × the density of the oil
(b) The fraction of oil displaced after immersing the object is 0.461 of the oil volume
Explanation:
(a) The volume, V of a cone of height, h and base diameter, D = 2×r is given by the following equation;

The volume of the object is therefore;

Where 6 cm is above the oil level we have;
above the oil level
Therefore, volume of the oil displaced =
cm³ = 216.11 cm³
The density of the object is thus;

The density of the object = 316/343 × the density of the oil.
(b) The volume of the oil = 2 × Volume of the object = 
The fraction of the volume displaced, x, after immersing the object is given as follows;

The fraction of oil displaced after immersing the object = 0.461 of the volume of the oil