Complete Question
The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader–a physicist, naturally–immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.08m. She sets the pendulum swinging, and her collaborators carefully count 101 complete cycles of oscillation during 2.00×102 s. What is the result? acceleration due to gravity:acceleration due to gravity: m/s2
Answer:
The acceleration due to gravity is
Explanation:
From the question we are told that
The length of the simple pendulum is 
The number of cycles is 
The time take is
Generally the period of this oscillation is mathematically evaluated as

substituting values


The period of this oscillation is mathematically represented as

making g the subject of the formula we have
![g = \frac{L}{[\frac{T}{2 \pi } ]^2 }](https://tex.z-dn.net/?f=g%20%3D%20%5Cfrac%7BL%7D%7B%5B%5Cfrac%7BT%7D%7B2%20%5Cpi%20%7D%20%5D%5E2%20%7D)

Substituting values

Answer:
a) t=24s
b) number of oscillations= 11
Explanation:
In case of a damped simple harmonic oscillator the equation of motion is
m(d²x/dt²)+b(dx/dt)+kx=0
Therefore on solving the above differential equation we get,
x(t)=A₀
where A(t)=A₀
A₀ is the amplitude at t=0 and
is the angular frequency of damped SHM, which is given by,

Now coming to the problem,
Given: m=1.2 kg
k=9.8 N/m
b=210 g/s= 0.21 kg/s
A₀=13 cm
a) A(t)=A₀/8
⇒A₀
=A₀/8
⇒
applying logarithm on both sides
⇒
⇒
substituting the values

b) 

, where
is time period of damped SHM
⇒
let
be number of oscillations made
then, 
⇒
Answer:
Top speed is 31.68 m/s
Explanation:
Speed of a body is the distance traveled by the body in unit time.
Speed is generally expressed in meter per second or kilometer per hour.
Here, the cheetah travels a distance of 274 m in 8.65 s.
Therefore, speed of cheetah is the distance traveled by it in one second.
For 8.65 s, distance traveled is 274 m
For 1 s, distance traveled will be
meters per second. This value is called speed.
So, speed is given as the ratio of the distance traveled to that of the time taken.
∴ Top speed of cheetah is given as:

Here,
is the top speed of cheetah.
Answer:
(a) 
(b) 
Given:
Time period of Pulsar, 
Equatorial radius, R = 15 Km = 15000 m
Spinning time, 
Solution:
(a) To calculate the value of the centripetal acceleration,
on the surface of the equator, the force acting is given by the centripetal force:

(1)
where

(2)
Now, from (1) and (2):



(b) To calculate the tangential acceleration of the object :
The tangential acceleration of the object will remain constant and is given by the equation of motion as:

where
u = 


