Answer
a) Using dimensional analysis we cannot derive the relation, But we can check the correctness of the formula.
now, L H S
s = distance
dimension of distance = [M⁰L¹T⁰]
now, equation on the right hand side
R H S
u = speed
u = m/s
Dimension of speed = [M⁰L¹T⁻¹]
dimension of time
t = sec
Dimension of time = [M⁰L⁰T¹]
Dimension of 'ut' = [M⁰L¹T⁻¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
now, acceleration= a
a = m /s²
dimension of acceleration = [M⁰L¹T⁻²]
dimension of (at²) = [M⁰L¹T⁻²][M⁰L⁰T¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
hence, the dimension are balanced.
so, L H S = R H S
b) Moment of inertia of hollow sphere =
Moment of inertia of solid sphere =
we know,
Torque is the force that causes rotation
If the same amount of torque is applied to both spheres the sphere with bigger moment of inertia would have smaller angular velocity.
Thus the solid sphere would accelerate more.
Explanation:
Inertia is the measure of the mass of an object. It is the tendency of an object to change the direction of an object.
Momentum is the product of mass and velocity. When an object having mass m moves with a particular velocity it will have momentum.
If the speed of an object is changed from u to v, its momentum can be changed and it can be calculated as :
Δp = m(v-u)
Hence, this is the required solution.
<h2>
Answer: (C) Radioactive dating</h2>
Explanation:
Let's begin by explaining that radioactive decay is a spontaneous process in which the nucleus of an atom disintegrates, giving way to the emission of radiation and the appearance of a new nucleus, releasing energy in the process.
<u>This process is widely used in</u><u> radioactive dating</u> (also called isotopic dating or radioisotope dating) in which radioactive impurities were selectively incorporated when the fossil materials were formed.
In this sense, when dating the age of the Earth and its components, it is useful to compare them with a naturally occurring radioisotope having a known half-life (generally uranium-238 is used and sometimes carbon-14).
Answer:
m1 = √2kg , m2 = 1kg , m3 = 1kg
Explanation:
Since the mass m1 can't move, the sum of horizontal and vertical forces must be zero. Since the mass m1 is suspended symmetrically the horizontal forces are equal if mass m2 and m3 are equal.
The tension in each string suspending mass m1 must match the force of gravity pulling on m1. The tension in each string is:
T = m2*g = m3*g = g
The vertical forces pulling m1 up is therefore: 2 * T * cos 45° = √2 * T = √2 * g
This force must match the force of gravity G pulling m1 down. G = m1 * g
Combining both equations: √2 * g = m1 * g
m1 = √2
Answer:
Transform Boundary
Explanation:
The just slide past each other