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Physics-

General

Easy

Question

A bob of mass m is suspended by a string from a train of mass M, free to move on a horizontal surface The bob is given a horizontal velocity V₀ The maximum height attained by the bob is

$\frac{V_{0}^{2}}{2 g} (\frac{M + m}{M})$
$\frac{V_{0}^{2} m}{2 g M}$
$\frac{V_{0}^{2} M}{2 g (M + m)}$
$\frac{V_{0}^{2}}{2 g}$

The correct answer is: $fraction numerator V subscript 0 end subscript superscript 2 end superscript M over denominator 2 g left parenthesis M plus m right parenthesis end fraction$

Apply COM, mV₀ = (M + m)V₂
Apply work energy theorem
DKE = W. D. by all forces
$fraction numerator 1 over denominator 2 end fraction left parenthesis m plus M right parenthesis V subscript 2 end subscript superscript 2 end superscript minus fraction numerator 1 over denominator 2 end fraction m V subscript 0 end subscript superscript 2 end superscript equals negative m g h$
$h equals fraction numerator V subscript 0 end subscript superscript 2 end superscript M over denominator 2 g left parenthesis M plus m right parenthesis end fraction$

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A small block is released from a point A of a rough semicircular track as shown in figure. When it moves along the track :

A small block is released from a point A of a rough semicircular track as shown in figure. When it moves along the track :

physics-General

A man standing on flat car under the shed of a small umbrella as shown in figure Rainfall starts at 30 m/s at an angle 30° with the vertical as shown. Find the speed and direction in which flatcar should be moved in order to save man from rain fall .

A man standing on flat car under the shed of a small umbrella as shown in figure Rainfall starts at 30 m/s at an angle 30° with the vertical as shown. Find the speed and direction in which flatcar should be moved in order to save man from rain fall .

physics-General

In the diagram shown, the rod is rigid and massless. A constant force F = mg has been applied vertically downwards on the rod The wall and the horizontal surface are perfectly smooth If the initial value of the angle $theta$ is equal to 45° then the minimum value of coefficient of friction between the blocks for on relative motion to start between the blocks, is equal to

In the diagram shown, the rod is rigid and massless. A constant force F = mg has been applied vertically downwards on the rod The wall and the horizontal surface are perfectly smooth If the initial value of the angle $theta$ is equal to 45° then the minimum value of coefficient of friction between the blocks for on relative motion to start between the blocks, is equal to

physics-General

parallel

A particle of mass m is projected at an angle of 60° with a velocity of 20 m/s relative to the ground from a plank of same mass m which is placed on smooth surface Initially plank was at rest The minimum length of the plank for which the ball will fall on the plank itself is

A particle of mass m is projected at an angle of 60° with a velocity of 20 m/s relative to the ground from a plank of same mass m which is placed on smooth surface Initially plank was at rest The minimum length of the plank for which the ball will fall on the plank itself is

physics-General

Statement‐I:: The values of a for which the point $left parenthesis a comma blank a to the power of 2 end exponent right parenthesis$ lies inside the triangle formed by the lines x=0, x+y=2, and 3y=x is (0,1) .
Statement‐II:: The parabola $y equals x to the power of 2 end exponent$ meets the line $x plus y equals 2$ at (1, 1) .

Statement‐I:: The values of a for which the point $left parenthesis a comma blank a to the power of 2 end exponent right parenthesis$ lies inside the triangle formed by the lines x=0, x+y=2, and 3y=x is (0,1) .
Statement‐II:: The parabola $y equals x to the power of 2 end exponent$ meets the line $x plus y equals 2$ at (1, 1) .

Tangents are drawn from the point (-1,2) on the parabola $y to the power of 2 end exponent equals 4 x$ The length, these tangents will intercept on the line $x equals 2$ :

Hence finally the length is $6 square root of 2$

Tangents are drawn from the point (-1,2) on the parabola $y to the power of 2 end exponent equals 4 x$ The length, these tangents will intercept on the line $x equals 2$ :

Hence finally the length is $6 square root of 2$

parallel

Let A and B be two points on a parabola $y to the power of 2 end exponent equals x$ with vertex V such that VA is perpendicular to VB and θ is the angle between the chord VA and the axis of the parabola The value of $fraction numerator vertical line V A vertical line over denominator vertical line V B vertical line end fraction$ is

Let A and B be two points on a parabola $y to the power of 2 end exponent equals x$ with vertex V such that VA is perpendicular to VB and θ is the angle between the chord VA and the axis of the parabola The value of $fraction numerator vertical line V A vertical line over denominator vertical line V B vertical line end fraction$ is

The equation of the parabola whose vertex and focus lie on the axis of $x$ at distances a and $a subscript 1 end subscript$ from the origin, respectively, is

The equation of the parabola whose vertex and focus lie on the axis of $x$ at distances a and $a subscript 1 end subscript$ from the origin, respectively, is

Consider, $L subscript 1 end subscript colon 2 x plus 3 y plus p minus 3 equals 0 semicolon L subscript 2 end subscript colon 2 x plus 3 y plus p plus 3 equals 0 comma$ where p is a real number, and $C colon x to the power of 2 end exponent plus y to the power of 2 end exponent plus 6 x minus 10 y plus 30 equals 0.$
Statement‐l:: If line $L subscript 1 end subscript$ is a chord of circle $C$ , then line $L subscript 2 end subscript$ is not always adiameter ofcircle C.
Statement‐II :: If line $L subscript 1 end subscript$ is a diameter ofcircle $C$ , then line $L subscript 2 end subscript$ is not a chord ofcircle C.

Consider, $L subscript 1 end subscript colon 2 x plus 3 y plus p minus 3 equals 0 semicolon L subscript 2 end subscript colon 2 x plus 3 y plus p plus 3 equals 0 comma$ where p is a real number, and $C colon x to the power of 2 end exponent plus y to the power of 2 end exponent plus 6 x minus 10 y plus 30 equals 0.$
Statement‐l:: If line $L subscript 1 end subscript$ is a chord of circle $C$ , then line $L subscript 2 end subscript$ is not always adiameter ofcircle C.
Statement‐II :: If line $L subscript 1 end subscript$ is a diameter ofcircle $C$ , then line $L subscript 2 end subscript$ is not a chord ofcircle C.

parallel

The equation of the circle passing through the points (1, 0) and (0,1) and having the smallest radius is:

Therefore the correct option is Choice 3

The equation of the circle passing through the points (1, 0) and (0,1) and having the smallest radius is:

Therefore the correct option is Choice 3

If a circle passes through the point (a, b) and cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals p to the power of 2 end exponent$ orthogonally, then the equation of the locus of its centre is‐

Hence locus of the given condition is optionD

If a circle passes through the point (a, b) and cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals p to the power of 2 end exponent$ orthogonally, then the equation of the locus of its centre is‐

Hence locus of the given condition is optionD

The square of the length of tangent from (3, -4) on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 4 x minus 6 y plus 3 equals 0$

Hence option C is correct

The square of the length of tangent from (3, -4) on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 4 x minus 6 y plus 3 equals 0$

Hence option C is correct

parallel

A hollow sphere of mass M and radius r is immersed in a tank of water (density r_w). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle 45° with the horizontal as shown in the figure. The tension T₁ in the wire is :

A hollow sphere of mass M and radius r is immersed in a tank of water (density r_w). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle 45° with the horizontal as shown in the figure. The tension T₁ in the wire is :

physics-General

A small wooden ball of density r is immersed in water of density $sigma$ to depth h and then released. The height H above the surface of water up to which the ball will jump out of water is

A small wooden ball of density r is immersed in water of density $sigma$ to depth h and then released. The height H above the surface of water up to which the ball will jump out of water is

physics-General

A dumbbell is placed in water of density r. It is observed that by attaching a mass m to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass m is negligible. The value of length l is

A dumbbell is placed in water of density r. It is observed that by attaching a mass m to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass m is negligible. The value of length l is

physics-General

parallel

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