Physics - Motion Plane - Quiz-2

An aeroplane is moving with a velocity u. It drops a packet from a height h. The time t taken by the packet in reaching the ground will be

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$\sqrt{(\frac{2 g}{h})}$
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$\sqrt{(\frac{2 u}{g})}$
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$\sqrt{(\frac{h}{2 g})}$
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$\sqrt{(\frac{2 h}{g})}$

An aeroplane is moving with horizontal velocity u at height h. The velocity of a packet dropped from it on the earth's surface will be (g is acceleration due to gravity)

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$\sqrt{u^{2} + 2 g h}$
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$\sqrt{2 g h}$
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2 gh
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$\sqrt{u^{2} - 2 g h}$

A bullet is fired with a speed of $1000 m / \sec$ in order to hit a target 100 m away. If $g = 10 m / s^{2}$ , the gun should be aimed:

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Directly towards the target
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5 cm above the target
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10 cm above the target
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15 cm above the target

A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from the rest at the top. How much time does it take to cover one-fourth distance starting from the rest at the top?

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1 s
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2 s
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4 s
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16 s

The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane 9.8 m long (angle of inclination is $30 °$ ) is:

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$\frac{1}{2} \sec$
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2 sec
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4 sec
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1 sec

A ball is dropped from the top of a tower of 100m height. Simultaneously another ball is thrown upwards from the bottom of the tower with a speed of 50 m/s ( $g = 10 m / s^{2}$ ). They will cross each other after:

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1 s
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2 s
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3 s
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4 s

Read the assertion and reason carefully to mark the correct option out of the options given below:

(5) If assertion is false but reason is true.

Assertion : Rocket in flight is not an illustration of projectile.

Reason : Rocket takes flight due to combustion of fuel and does not move under the gravity effect alone.

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If both assertion and reason are true and the reason is the correct explanation of the assertion.
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If both assertion and reason are true but reason is not the correct explanation of the assertion.
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If assertion is true but reason is false.
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If the assertion and reason both are false.

If the body is moving in a circle of radius r with a constant speed v, its angular velocity is:

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v/r
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r/v
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v²/r
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vr

Two racing cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

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m₁ : m₂
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r₁ : r₂
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1 : 1
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m₁ r₁ : m₂ r₂

If a particle moves in a circle describing equal angles in equal times, its velocity vector:

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remains constant.
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changes in magnitude.
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changes in direction.
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changes both in magnitude and direction.

A motorcyclist going round in a circular track at a constant speed has:

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constant linear velocity.
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constant acceleration.
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constant angular velocity.
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constant force.

A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio

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1 : 1
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1 : 2
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2 : 1
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4 : 1

A particle moves with constant angular velocity in a circle. During the motion its

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Energy is conserved
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Momentum is conserved
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Energy and momentum both are conserved
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None of the above is conserved

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is

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R/r
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r/R
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R²/r²
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r²/R²

A particle is moving in a horizontal circle with constant speed. It has constant

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Velocity
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Acceleration
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Kinetic energy
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Displacement

The angular speed of a flywheel making 120 revolutions/minute is:

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$2 π r a d / s$
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$4 π^{2} r a d / s$
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$π r a d / s$
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$4 π r a d / s$

Certain neutron stars are believed to be rotating at about 1 rev/sec. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be

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$20 \times 10^{8} m / \sec^{2}$
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$8 \times 10^{5} m / \sec^{2}$
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$120 \times 10^{5} m / \sec^{2}$
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$4 \times 10^{8} m / \sec^{2}$

An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m, the acceleration of a point on the tip of the blade is about

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1600 m/sec²
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4740 m/sec²
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2370 m/sec²
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5055 m/sec²

The angular speed of seconds needle in a mechanical watch is:

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$\frac{π}{30}$ rad/s
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2π rad/s
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π rad/s
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$\frac{60}{π}$ rad/s

What is the value of linear velocity if $\vec{ω} = 3 \hat{i} - 4 \hat{j} + \hat{k}$ and $\vec{r} = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$

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$6 \hat{i} + 2 \hat{j} - 3 \hat{k}$

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$- 18 \hat{i} - 13 \hat{j} + 2 \hat{k}$

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$4 \hat{i} - 13 \hat{j} + 6 \hat{k}$

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$6 \hat{i} - 2 \hat{j} + 8 \hat{k}$

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is:

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$2 π v / T$

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$2 π r / T$

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$2 π r^{2} / T$

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$2 π v^{2} / T$

If the range of a gun that fires a shell with muzzle speed v is R, then the angle of elevation of the gun is

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$\cos^{- 1} (\frac{v^{2}}{R g})$

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$\cos^{- 1} (\frac{g R}{v^{2}})$

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$\frac{1}{2} (\frac{v^{2}}{R g})$

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$\frac{1}{2} \sin^{- 1} (\frac{g R}{v^{2}})$

In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m (see figure). The magnitude of the average velocity is

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3.14 m/s

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2.0 m/s

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1.0 m/s

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Zero

A stone ties to the end of a string 1m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone

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$\frac{π^{2}}{4} m s^{- 2}$ and direction along the radius towards the centre

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$π^{2} m s^{- 2}$ and direction along the radius away from the centre

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$π^{2} m s^{- 2}$ and direction along the radius towards the centre

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$π^{2} m s^{- 2}$ and direction along the tangent to the circle

If the equation for the displacement of a particle moving on a circular path is given by $(θ) = 2 t^{3} + 0 .5$ , where θ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is:

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8 rad/sec

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12 rad/sec

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24 rad/sec

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36 rad/sec

For a particle in a non-uniform accelerated circular motion

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Velocity is radial and acceleration is transverse only

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Velocity is transverse and acceleration is radial only

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Velocity is radial and acceleration has both radial and transverse components

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Velocity is transverse and acceleration has both radial and transverse components

The coordinates of a moving particle at any time ‘t’ are given by x = αt³ and y = βt³. The speed of the particle at time ‘t’ is given by:

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$\sqrt{α^{2} + β^{2}}$

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$3 t \sqrt{α^{2} + β^{2}}$

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$3 t^{2} \sqrt{α^{2} + β^{2}}$

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$t^{2} \sqrt{α^{2} + β^{2}}$

The figure shows a body of mass m moving with a uniform speed v along a circle of radius r. The change in velocity in going from A to B is:

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$v \sqrt{2}$

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$v / \sqrt{2}$

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v

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zero

A particle moves in a circular path with decreasing speed. Choose the correct statement.

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Angular momentum remains constant

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Acceleration ( $\vec{a}$ ) is towards the center

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Particle moves in a spiral path with decreasing radius

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The direction of angular momentum remains constant

The angle turned by a body undergoing circular motion depends on time as $θ = θ_{0} + θ_{1} t + θ_{2} t^{2}$ . Then the angular acceleration of the body is

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θ₁

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θ₂

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2θ₁

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2θ₂

0:0:1

0:0:1

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