Pseudo Force

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JEE Main 2021, 26 Feb Shift-I

A person standing on a spring balance inside a stationary lift measures $60 kg$ . The weight of that person, if the lift descends with uniform downward acceleration of $1.8 m/s^{2}$ will be ......... $N$ . $[g = 10 m/s^{2}]$

A block is kept on a frictionless inclined surface with angle of inclination $α$ . The incline is given an acceleration $a$ to keep the block stationary. Then, $a$ is equal to

\frac{g}{t a n α}

(B)

g cosec α

(C)

g

(D)

g tan α

LEVELJEE Main

A lift is moving down with acceleration $a$ . A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively

(A)

g, g

(B)

g - a, g - a

(C)

g - a, g

(D)

a, g

JEE Main 2021, 1 Sep Shift-II

LEVELJEE Advanced

A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is [Given, $m = 8 kg, M = 16 kg$ ] Assume all the surfaces shown in the figure to be frictionless.

(A)

\frac{4}{3} g

(B)

\frac{6}{5} g

(C)

\frac{3}{5} g

(D)

\frac{2}{3} g

JEE Main 2021, 31 Aug Shift-I

LEVELJEE Main

A car is moving on a plane inclined at $3 0^{\circ}$ to the horizontal with an acceleration of $10 ms^{- 2}$ parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ......... (Take, $g = 10 ms^{- 2}$ )

JEE Advanced 2016

LEVELJEE Advanced

Comprehension Passage

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity

ω

is an example of a non-inertial frame of reference. The relationship between the force

F_{rot}

experienced by a particle of mass

m

moving on the rotating disc and the force

F_{in}

experienced by the particle in an inertial frame of reference is,

F_{rot} = F_{in} + 2 m (v_{rot} \times ω) + m (ω \times r) \times ω

, where,

v_{rot}

is the velocity of the particle in the rotating frame of reference and

r

is the position vector of the particle with respect to the centre of the disc. Now, consider a smooth slot along a diameter of a disc of radius

R

rotating counter-clockwise with a constant angular speed

ω

about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the

X

-axis along the slot, the

Y

-axis perpendicular to the slot and the

z

-axis along the rotation axis (

ω = ω \hat{k}

). A small block of mass

m

is gently placed in the slot at

r = (R /2) \hat{i}

t = 0

and is constrained to move only along the slot.

Question 1:

LEVELJEE Advanced

A circular disc with a groove along its diameter is placed horizontally. A block of mass $1 kg$ is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $μ = \frac{2}{5}$ . The disc has an acceleration of $25 m/s^{2}$ . Find the acceleration of the block with respect to disc. Given $cos θ = \frac{4}{5}$ .

LEVELJEE Advanced

A piece of wire is bent in the shape of a parabola $y = k x^{2}$ ( $y$ -axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$ -axis with a constant acceleration $a$ . The distance of the new equilibrium position from the $y$ -axis of the bead, where the bead can stay at rest with respect to the wire,

(A)

\frac{a}{g k}

(B)

\frac{a}{2 g k}

(C)

\frac{2 a}{g k}

(D)

\frac{a}{4 g k}

LEVELJEE Main

A reference frame attached to the earth (1986)

* Multiple Correct Options

(A)

is an inertial frame by definition

(B)

cannot be an inertial frame because the earth is revolving round the sun

(C)

is an inertial frame because Newton's laws are applicable in this frame

(D)

cannot be an inertial frame because the earth is rotating about its own axis

LEVELJEE Advanced

System shown in figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass $2 m$ and $m$ just after the string is cut will be (2006)

(A)

\frac{g}{2}

upwards,

g

downwards

(B)

g

upwards,

\frac{g}{2}

downwards

(C)

g

upwards,

2 g

downwards

(D)

2 g

upwards,

g

downwards

JEE Advanced 2016

LEVELJEE Advanced

Comprehension Passage

ω

is an example of a non-inertial frame of reference. The relationship between the force

F_{rot}

experienced by a particle of mass

m

moving on the rotating disc and the force

F_{in}

experienced by the particle in an inertial frame of reference is

F_{rot} = F_{in} + 2 m (v_{rot} \times ω) + m (ω \times r) \times ω

, where

v_{rot}

is the velocity of the particle in the rotating frame of reference and

r

is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter of a disc of radius

R

rotating counter-clockwise with a constant angular speed

ω

about its vertical axis through its center. We assign a coordinate system with the origin at the centre of the disc, the x-axis along the slot, the y-axis perpendicular to the slot and the z-axis along the rotation axis (

ω = ω \hat{k}

). A small block of mass

m

is gently placed in the slot at

r = (R /2) \hat{i}

t = 0

and is constrained to move only along the slot.

Question 1:

The distance $r$ of the block at time $t$ is :

(A)

\frac{R}{4} (e^{2 ω t} + e^{- 2 ω t})

(B)

\frac{R}{2} cos 2 ω t

(C)

\frac{R}{2} cos ω t

(D)

\frac{R}{4} (e^{ω t} + e^{- ω t})

Question 2:

The net reaction of the disc on the block is :

(A)

- m ω^{2} R cos ω t \hat{j} - m g \hat{k}

(B)

m ω^{2} R sin ω t \hat{j} - m g \hat{k}

(C)

\frac{1}{2} m ω^{2} R (e^{ω t} - e^{- ω t}) \hat{j} + m g \hat{k}

(D)

\frac{1}{2} m ω^{2} R (e^{2 ω t} - e^{- 2 ω t}) \hat{j} + m g \hat{k}

JEE Advanced 2025

LEVELJEE Main

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height $y$ (in m) of the elevator, from the ground, with time $t$ (in s) is given by $y = 8 [1 + sin (\frac{2 π t}{T})]$ , where $T = 40 π$ s. Taking acceleration due to gravity, $g = 10 m/s^{2}$ , the maximum variation of the object's weight (in N) as observed in the experiment is _______.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then, a is equal to

Comprehension Passage

A reference frame attached to the earth (1986)

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The distance r of the block at time t is :

The net reaction of the disc on the block is :

A block is kept on a frictionless inclined surface with angle of inclination $α$ . The incline is given an acceleration $a$ to keep the block stationary. Then, $a$ is equal to

The distance $r$ of the block at time $t$ is :