Elements with atomic numbers above 95 are called ____

Suppose that a balloon is being filled with air at a rate of 10 cm3/s. (Assume that theballoon is a perfect sphere.) At what rat

Basile [38]

Answer:

Therefore the surface area of the balloon is increased at 4 cm³/s.

Explanation:

The balloon is being filled with air at a rate of 10 cm³/s

It means the volume of the balloon is increased at a rate 10 cm³/s.

i.e $\frac{dv}{dt} =10 cm^3/s$

Consider r be the radius of the balloon.

The volume of of a sphere is

$v=\frac{4}{3} \pi r^3$

Differentiate with respect to t

$\frac{dv}{dt} =\frac{4}{3} \pi \times 3r^2\frac{dr}{dt}$

$\Rightarrow 10 =4\pi r^2\frac{dr}{dt}$

$\Rightarrow \frac{dr}{dt}=\frac{10}{4\pi r^2}$

The surface of area of the balloon is(S) = $4\pi r^2$

$S=4\pi r^2$

Differentiate with respect to t

$\frac{dS}{dt} =4\pi\times2r\frac{dr}{dt}$

$\Rightarrow \frac{dS}{dt} =8\pi r\frac{dr}{dt}$

Putting the value of $\frac{dr}{dt}$

$\Rightarrow \frac{dS}{dt} =8\pi r\times\frac{10}{4\pi r^2}$

$\Rightarrow \frac{dS}{dt} =\frac{20}{ r}$

Given that r = 5 cm

$[\frac{dS}{dt}]_{r=5} =\frac{20}{ 5}$ =4 cm³/s

Therefore the surface area of the balloon is increased at 4 cm³/s.

5 0

4 years ago

Fill in the blank. Consider the inverse square law: When light leaves a light bulb, it spreads out over more and more space as i

aliya0001 [1]

Answer:

Explanation:

Intensity of light is inversely proportional to distance from source

I ∝ 1 /r² where I is intensity and r is distance from source . If I₁ and I₂ be intensity at distance r₁ and r₂ .

I₁ /I₂ = r₂² /r₁²

If r₂ = 4r₁ ( given )

I₁ / I₂ = (4r₁ )² / r₁²

= 16 r₁² / r₁²

I₁ / I₂ = 16

I₂ = I₁ / 16

So intensity will become 16 times less bright .

"16 times " is the answer .

8 0

3 years ago

A car is traveling 16 m/s East. If the car then speeds up at a constant acceleration, what is the direction of the car’s acceler

konstantin123 [22]

The direction is east since its constant

8 0

3 years ago

Q.By the method of dimensional analysis derive the

Artyom0805 [142]

Answer

a) Using dimensional analysis we cannot derive the relation, But we can check the correctness of the formula.

$s = u t +\dfrac{1}{2}at^2$

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 = $\dfrac{2}{3}Mr^2$

Moment of inertia of solid sphere = $\dfrac{2}{5}Mr^2$

we know,

$\tau = I \alpha$

$\alpha=\dfrac{\tau}{I}$

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.

4 0

3 years ago

Read 2 more answers

If car A passes car B, then car A must be

Tcecarenko [31]

Answer:

B. moving faster than car B, but not necessarily accelerating

Explanation:

Velocity is the speed of something. So car A's velocity is greater than car B but does not mean car A is accelerating.

4 0

3 years ago

Elements with atomic numbers above 95 are called _____ elements