Answer:
The block's mass should be 
Explanation:
Given:
Cart with mass 
From the conservation of energy before mass is added,

Where
amplitude of spring mass system,
spring constant

Now new mass
is added to the system,


Here, given in question frequency is reduced to half so we can write,

Where
frequency of system before mass is added,
frequency of system after mass is added.




Therefore, the block's mass should be 
Answer:

Explanation:
Impulse-Momentum relation:


We solve the equations in order to find the braking force:

The correct statements are that the speed decreases as the distance decreases and speed increases as the distance increases for the same time.
Answer:
Option A and Option B.
Explanation:
Speed is defined as the ratio of distance covered to the time taken to cover that distance. So Speed = Distance/Time. In other words, we can also state that speed is directly proportional to the distance for a constant time. Thus, the speed will be decreasing as there is decrease in distance for the same time. As well as there will be increase in speed as the distance increases for the same time. So option A and option B are the true options. So if there is decrease in the distance due to direct proportionality the speed will also be decreasing. Similarly, if the distance increases, the speed will also be increasing.
Answer:
r = 6.4 cm
Explanation:
F = GMm/r²
r = √(GMm/F)
r = √((6.674e-11)(6.2e5)(13e3)/130)
r = 0.06432... m
Those are some high density materials!
The Young modulus E is given by:

where
F is the force applied
A is the cross-sectional area perpendicular to the force applied

is the initial length of the object

is the increase (or decrease) in length of the object.
In our problem,

is the initial length of the column,

is the Young modulus. We can find the cross-sectional area by using the diameter of the column. In fact, its radius is:

and the cross-sectional area is

The force applied to the column is the weight of the load:

Now we have everything to calculate the compression of the column:

So, the column compresses by 1.83 millimeters.