Explanation:
Let us assume that the final resistance after stretching is
. Since, the volume of rod does not change and the initial and final volume will be the same as follows.
V = 

It is given that,
.
Therefore, 


We know that relation between resistance and area is as follows.
R = 

= 
= 9
= 9R
Thus, we can conclude that the resistance of the stretched wire is 9R.
Answer:
option (d) 7.1 kN
Explanation:
Given:
Mass of the car, m = 1600 kg
Acceleration of the car, a = 1.5 m/s²
Coefficient of kinetic friction = 0.3
let the tension be 'T'
Now,
ma = T - f .................(1)
where f is the frictional force
also,
f = 0.3 × mg
where g is the acceleration due to the gravity
thus,
f = 0.3 × 1600 × 9.81 =
therefore,
equation 1 becomes
1600 × 1.5 = T - 4708.8
or
T = 2400 + 4708.8
or
T = 7108.8 N
or
T = 7.108 kN
Hence,
The correct answer is option (d) 7.1 kN
The inverse hyperbolic cosecant of anything is a negative number.
In particular, csch⁻¹ [ (-1)/(2√30) ] = csch⁻¹ (≈ -0.0913) = ≈ -3.089
Whatever it is, negative numbers don't have logarithms.
Answer:
Resultant displacement = 38.58 miles at an angle of 23.57° north of west.
Explanation:
Let north represent positive y direction and east represent positive x direction. Unit vector along x direction is represented by i and vector along unit vector along y direction is represented by j
Initial displacement = 17 miles north = 17 j miles
Final displacement = 24 miles at an angle of 40° west of north = 24 miles at an angle of 130° to positive x -axis
= (24 cos 130 i + 24 sin 130 j )
= (-15.43 i + 18.36 j ) miles
Total displacement = 17 j + (-15.43 i + 18.36 j) = -15.43 i + 35.36 j
Magnitude of displacement 
Angle to positive x -axis = tan⁻¹(35.36/-15.43) = 113.57°
Resultant displacement = 38.58 miles at an angle of 23.57° west of north.
Answer:
Beyond our solar system, organic molecules have been found in giant clouds of dust and gas between stars and in star-forming regions.
In our solar system, besides Earth, organic molecules have been discovered on comets, in meteorites, on Saturn's moon Titan, in the plumes of water expelled from Saturn's moon Enceladus, and on Neptune's moon Triton.