Class 11th

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :
(Diagram shows ball 'a' hitting the wall perpendicularly along the x-axis and ball 'b' hitting the wall at a 45° angle to the x-axis.)

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Class 11th Physics Motion in Straight Line

Contributor-Level 9

For ball (a): I? = Δp? = 2mu
For ball (b): I? = Δp? = 2mu cos 45°
I? /I? = 2mu / (2mu cos 45°) = √2

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3 months ago

The relation between time t and distance x for a moving body is given as t = mx² + nx, where m and n are constants. The retardation of the motion is: (Where v stands for velocity)

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Contributor-Level 10

By t = mx² + nx
dt/dx = 2mx + n
V = dx/dt = 1/ (2mx + n)
a = v (dv/dx) = V (d/dx (1/ (2mx+n) = V [-2m/ (2mx+n)²] = -2mV³
So, Retardation will be (2mv³)

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3 months ago

Two vectors X and Y have equal magnitude. The magnitude of (X - Y) is n times the magnitude of (X + Y). The angle between X and Y is :

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Class 11th Physics Motion in Straight Line

Contributor-Level 10

According to question
|x| = |y| and
|x - y| = n|x + y|
x² + y² - 2x·y = n² (x² + y² + 2x·y)
(1 - n²) (x² + y²) = (1 + n²)2x·y
(1 - n²) (x² + y²) = (1 + n²)2xy cosθ
(1 - n²) (2x²) = (1 + n²) (2x²)cosθ
cos θ = (1 - n²)/ (1 + n²)
θ = cos? ¹ (1 - n²)/ (1 + n²) = cos? ¹ (- (n²-1)/ (n²+1)

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3 months ago

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4? second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap? (Take g = 9.8 m/s²)

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Class 11th Physics Motion in Straight Line

Contributor-Level 9

Displacement in 4? second
= S? - S?
= (1/2)g [2n - 1]
= (1/2)g [2*4 - 1]
= (1/2) * 9.8 * 7
= 34.3m
As this distance matches with data given in question for position of next drop. So drops are falling at the rate of 1 drop/second.

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3 months ago

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around :
(takes the value of g as 10 m/s²)

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Contributor-Level 10

Body is dropped from height 75m with initial velocity (upward) 10m/s
So, s = ut + ½ at²
-75 = 10t - ½ gt²
5t² - 10t - 75 = 0
By solving t = 5 sec.
In 5sec. balloon covered
h = 10 * 5 = 50m
Now height of balloon = 75 + 50 = 125m

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3 months ago

The minimum and maximum distances of a planet revolving around the Sun are x? and x?. If the minimum speed of the planet on its trajectory is v?, then its maximum speed will be :

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New answer posted

3 months ago

Match List I with List II.

List - I	List - II
(a) C - A - B = 0	(i) Diagram showing A + B = C
(b) A - C - B = 0	(ii) Diagram showing C + B = A
(c) B - A - C = 0	(iii) Diagram showing A + C = B
(d) A + B = -C	(iv) Diagram showing A + B + C = 0

Choose the correct answer from the options given below :

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Contributor-Level 9

From triangle law of addition, we can clearly write answer.

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3 months ago

Class 11th Ncert Solutions Maths class 11th

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Moment of inertia of a circular disc 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be I?, I? & I? respectively. The respective radii of gyration about all the three axes will be the same.

Reason R: A rigid body making rotational motion has fixed mass and shape.

In the light of the above statements, choose the most appropriate answer from the options given below:

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New answer posted

3 months ago

The number of distinct real roots of x4 – 4x + 1 = 0 is:

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Class 11th Physics Mechanical Properties of Solids

Contributor-Level 9

$f (x) = x^{4} - 4 x + 1 = 0$

$f' (x) = 4 x^{3} - 4$

$= 4 (x - 1) (x^{2} + 1 + x)$

$\Rightarrow$ Two solution

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3 months ago

If y, K and $η$ are the value of Young's modulus, bulk modulus of rigidity of any material respectively. Choose

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