Basic Science Test 14

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Basic Science Test 14

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Weekly Quiz Competition

Question 1
1 / -0

If a body starts from rest and travel $$120m$$ in the $$8^{th}$$ seconds, then acceleration is:

A
$$16\ m/s^2$$

B
$$10\ m/s^2$$

C
$$0.227\ m/s^2$$

D
$$0.03\ m/s^2$$

Solution

Wevknow that
$$S_{n^{th}}=u+\dfrac{a}{2}(2n-1)$$
$$\Rightarrow 120=S_{8^{th}}=0+\dfrac{a}{2}(2\times 8-1)$$
$$\Rightarrow =\dfrac{240}{15}=\dfrac{80}{5}=16m/s^2$$
Question 2
1 / -0

Which temperature is same on centigrade as well as on Fahrenheit scale?

A
$$40$$

B
$$-40$$

C
Both

D
None

Solution

$$F=\left(\dfrac{9}{5}\right)C+32$$

as $$F=C$$

$$C=\left(\dfrac{9}{5}\right)C+32$$

$$C-\dfrac{9}{5}C=32$$

$$\dfrac{-4C}{5}=32$$

$$C=-40$$
Question 3
1 / -0

The coefficient of static friction between the box and the train's floor is $$0.2$$. The maximum acceleration of the train in which a box lying on its floor with remain stationary is
(Take $$g=10\ m\ s^{-2}$$)

A
$$2\ ms^{-2}$$

B
$$4\ ms^{-2}$$

C
$$6\ ms^{-2}$$

D
$$8\ ms^{-2}$$

Solution

Trun is moving forced. So, preudo form on box will be backward friction will be in forward
$$ma=\mu mg$$
$$a=\mu g$$
$$=0.2\times 10$$
$$=2\ m/s^{2}$$
Question 4
1 / -0

In a boat of mass $$4\ M $$ length $$'L'$$ on a frictionless water surface. Two men A (mass = $$M$$) B (mass $$ = 2M $$) are standing on the opposite ends. Now A travels a distance $$ \dfrac{L}{4} $$ relative to boat towards its center and B moves a distance $$ \dfrac{3L}{4} $$ relative to boat and meet A. The displacement of the boat on water till A and B meet is

A
$$ \dfrac{5L}{28} $$

B
Zero

C
$$ \dfrac{L}{2} $$

D
$$ \dfrac{23L}{2} $$

Solution

COM will remain
$$ MX_{0} + 4M \left (\dfrac{L}{2} \right ) + 2M (L) = X_{COM} $$

Now
$$ M \left (\dfrac{L}{4} - x \right ) + 4M \left (\dfrac{L}{2} - x \right ) + 2M \left (\dfrac{L}{4} - x \right ) = X_{COM} $$

$$ \dfrac{4ML}{2} + 2ML = M \left (\dfrac{L}{4} - x \right ) + 4M \left (\dfrac{L}{2} - x \right ) + 2M \left (\dfrac{L}{4} - x \right ) $$

$$4L = \dfrac{3L}{4} - 3x + \dfrac{4L}{2} - 4x $$

$$2L - \dfrac{3L}{4} = -7x \Rightarrow \dfrac{8L - 3L}{4} = 7x $$

$$ \boxed{x = \dfrac{5L}{28}} $$
Question 5
1 / -0

In a rotor, a hollow vertical cyclinderical structure rotates about its axis and a person rests against the the inner wall. At a particular speed of the rotor, the floor below the person is removed and the person hangs resting against the wall without any floor. If athe radius of the rotor is $$2m$$ and the coefficient of static friction between the wall and the person is $$0.2$$ find the minimum speed at which the floor may be removed Take $$g=10\ m/s^2$$

A
$$10m/s$$

B
$$20m/s$$

C
$$100m/s$$

D
$$50m/s$$

Solution

We know that
$$V=\sqrt{\dfrac{R_g}{\mu}}=\sqrt{\dfrac{20}{0.2}}=10m/s$$
Question 6
1 / -0

A particle of mass $$1\ gm $$ executes an oscillatory motion on the concave surface of a spherical dish of radius $$2\ m $$ placed on a horizontal plane. If the motion of the particle begins from a point on the dish at a height of $$1\ cm $$ from the horizontal plane and the coefficient of friction is $$0.01$$, the total distance covered by the particle before it comes to rest is :

A
$$100.5\ m $$

B
$$10.05\ m $$

C
$$1.005\ m $$

D
$$0.1005\ m $$

Solution

$$m = 1\ g , R = 2\ m , h = 1\ cm $$
$$ r = 0.01 $$
PE is high
$$W = \mu R d = \mu mg d $$

PE is spent in doing work
$$ \mu mg \times d = mgh $$
$$ d = \dfrac{h}{\mu} = \dfrac{1}{0.01} = 100\ cm = 1\ m $$
Question 7
1 / -0

The particles A and B of mass m each are separated by a distance $$r$$. Another particle C of mass M is placed at the midpoint of A and B. Find the work done in taking C to a point equidistant r from A and B without acceleration (G= Gravitational constant and only gravitational interaction between A, B and C is considered)

A
$$ \dfrac{GMm}{r} $$

B
$$ \dfrac{2GMm}{r} $$

C
$$ \dfrac{3GMm}{r} $$

D
$$ \dfrac{4GMm}{r} $$

Solution

According to question we have
$$U_{i} = \dfrac{-GMm}{r/2} - \dfrac{GMm}{r/2} = - \dfrac{4GMm}{r} $$

$$U_{f} = \dfrac{-GMm}{r} - \dfrac{GMm}{r} = \dfrac{-2GMm}{r} $$

$$ \therefore $$ Work done $$ = U_{f} - U_{i} = \dfrac{2GMm}{r} $$
Question 8
1 / -0

A ball is thrown from the ground with velocity u at an angle $$ \theta $$ with horizontal. The horizontal range of the ball on the ground is $$ R $$. If the coefficient of restitution is $$ e $$, then the horizontal range after the collision is

A
$$ e^{3}R $$

B
$$ e^{2}R $$

C
$$ eR $$

D
$$ \frac{R}{e} $$

Solution

$$ R = \dfrac{4^{2} sin^ {2} \theta}{g} = \dfrac{24^{2} sin \theta cos \theta}{g} $$ ...........................(1)
$$ Vy^{1} = eVy = eusin \theta $$
After collision
$$ Vy^{1} = eusin \theta$$
$$ T = \dfrac{2Vy^{1}}{g} = \dfrac{2eusin \theta}{g}\cdot ucos \theta $$
$$ = e \dfrac{24^{2} sin \theta cos \theta}{g} $$
$$ R^{1} = eR $$
Question 9
1 / -0

A body of mass $$5\ kg$$ explodes at rest into three fragments with masses in the ratio $$1:1:3$$. The fragments with equal masses fly in mutually perpendicular directions with speeds of $$21\ m/s$$. The velocity of heaviest fragment in $$m/s$$ will be

A
$$7\sqrt 2$$

B
$$5\sqrt 2$$

C
$$3\sqrt 2$$

D
$$\sqrt 2$$

Solution

$$5\ kg$$
$$1:1:3$$
initially momentum $$=0$$
$$0=21 \hat i +21j +3(v)$$
$$\sqrt{21+21^2}=21\sqrt 2$$
$$0=|21\sqrt 2|+3(v)$$
$$0=7\sqrt 2+v$$
$$v=| 7\sqrt 2|$$
$$=7\sqrt 2\ m/s$$
Question 10
1 / -0

A particle moves in a straight line and its speed depends on time as $$v=|2t-3|\cdot\int vdt$$ represents the distance traveled of the particle then find the displacement of the particle in $$5s$$

A
$$65m$$

B
$$12.25m$$

C
$$2.25m$$

D
$$14.5m$$

Solution

$$V=\int_{(2t-3)}^{-(3t-3)}0\leq t <\frac{3}{2}$$
$$=\int vdt=-\int_{0}^{\frac{3}{2}}(2t-3)dt+\int_{\frac{3}{2}}^{5}(+2t-3)dt$$
$$=-[t^2-3t]\int_{\frac{3}{2}}^{0}+[+t^2-3t]\int_{\frac{3}{2}}^{5}$$
$$=-\frac{9}{4}+\frac{9}{2}+25-15-\frac{9}{4}+\frac{9}{2}$$
$$=10+\frac{9}{2}=\frac{29}{2}=14.5$$

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Re-Attempt Weekly Quiz Competition

Basic Science Test 14

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Basic Science Test 14

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SHARING IS CARING

Question 1

$$16\ m/s^2$$

$$10\ m/s^2$$

$$0.227\ m/s^2$$

$$0.03\ m/s^2$$

Solution

Question 2

$$40$$

$$-40$$

Both

None

Solution

Question 3

$$2\ ms^{-2}$$

$$4\ ms^{-2}$$

$$6\ ms^{-2}$$

$$8\ ms^{-2}$$

Solution

Question 4

$$ \dfrac{5L}{28} $$

Zero

$$ \dfrac{L}{2} $$

$$ \dfrac{23L}{2} $$

Solution

Question 5

$$10m/s$$

$$20m/s$$

$$100m/s$$

$$50m/s$$

Solution

Question 6

$$100.5\ m $$

$$10.05\ m $$

$$1.005\ m $$

$$0.1005\ m $$

Solution

Question 7

$$ \dfrac{GMm}{r} $$

$$ \dfrac{2GMm}{r} $$

$$ \dfrac{3GMm}{r} $$

$$ \dfrac{4GMm}{r} $$

Solution

Question 8

$$ e^{3}R $$

$$ e^{2}R $$

$$ eR $$

$$ \frac{R}{e} $$

Solution

Question 9

$$7\sqrt 2$$

$$5\sqrt 2$$

$$3\sqrt 2$$

$$\sqrt 2$$

Solution

Question 10

$$65m$$

$$12.25m$$

$$2.25m$$

$$14.5m$$

Solution

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