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Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always threethree times its height. Supp

hammer [34]

Answer:

159241.048 cm³/s

Explanation:

r = Radius = 3×height = 3h

h = height = 16 cm

Height of the pile increases at a rate = $\frac{dh}{dt}=22\ cm/s$

$\text{Volume of cone}=\frac{1}{3}\pi r^2h\\\Rightarrow V=\frac{1}{3}\pi (3h)^2h\\\Rightarrow V=3\pi h^3$

Differentiating with respect to time

$\frac{dv}{dt}=9\pi h^2\frac{dh}{dt}\\\Rightarrow \frac{dv}{dt}=9\pi 16^2\times 22\\\Rightarrow \frac{dv}{dt}=159241.048\ cm^3/s$

∴ Rate is the sand leaving the bin at that instant is 159241.048 cm³/s

5 0

2 years ago

A bullet is dropped into a river from a very high bridge. At the same time, another bullet is fired from a gun straight down tow

anastassius [24]

Answer:

Option (c)

Explanation:

Both the bullets have same acceleration because they both falls under the influence of acceleration due to gravity.

The bullet which is fired from the gun has some initial velocity but the bullet which is dropped has zero initial velocity.

the acceleration is acting on both the bullets which is equal to the acceleration due to gravity and they both in motion in the influence of gravity.

8 0

2 years ago

A wire has a cross sectional area of 4.00 mm2 and is stretched by 0.100 mm by a certain force. How far will a wire of the same m

Nina [5.8K]

Answer: $0.05\ mm$

Explanation:

Given

Cross-sectional area of wire $A_1=4\ mm^2$

Extension of wire $\delta l=0.1\ mm$

Extension in a wire is given by

$\Rightarrow \delta l=\dfrac{FL}{AE}$

where, $E=\text{Youngs modulus}$

$\Rightarrow \delta_1=\dfrac{FL}{A_1E}\quad \ldots(i)$

for same force, length and material

$\Rightarrow \delta_2=\dfrac{FL}{A_2E}\quad \ldots(ii)$

Divide (i) and (ii)

$\Rightarrow \dfrac{0.1}{\delta_2}=\dfrac{A_2}{A_1}\\\\\Rightarrow \delta_2=0.1\times \dfrac{4}{8}\\\\\Rightarrow \delta_2=0.05\ mm$

5 0

2 years ago

An object is moving on a horizontal frictionless surface. if the net force applied to the object in the direction of motion is d

sukhopar [10]

Answer:

doubled

Explanation:

F=ma1----------(1)

2F = ma2-------(2)

Divide 2nd equation by 1st one

we get a1×2=a2

5 0

1 year ago

A series of bright fringes appears on the viewing screen of a Young's double-slit experiment. Suppose you move from one bright f

goblinko [34]

Ahahaha fidjdsd skssjsjsbs SJSU’s

6 0

2 years ago