Earth as Inertial Frame

Q.

The mass of a lift is $500kg$. What will be the tension in its cable if it moves down with an acceleration $2m{s}^{-2}$?

Q.

Mass of wedge as shown in figure is M and that of the block is m. Neglecting friction at all the places and mass of the pulley, calculate acceleration of the wedge. Thread is inextensible.

1. $\frac{mgsin\theta }{M+m(1-cos\theta )}$

2. $\frac{mgsin\theta }{M+2m(1-cos\theta )}$

3. $\frac{M+m(1-cos\theta )g}{msin\theta }$

4. mg sin$\theta$

Q.

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of $5m/s^2$, the reading of the spring balance will be:

1. 74 N

2. 15 N

3. 49 N
4. 24 N

Q. Inner and outer radii of a spool are $r$ and $\text{R}$, respectively. A thread is wound over its inner surface and spool is placed over a rough horizontal surface. Thread is pulled by a force $\text{F}$ as shown in Fig. In case of pure rolling, which of the following statements are false?

1. Thread unwinds, spool rotates anticlockwise and friction acts leftwards.
2. Thread winds, spool rotates clockwise and friction acts leftwards.
3. Thread winds, spool moves to the right and friction acts rightwards.
4. Thread winds, spool moves to the right and friction does not come into existence.

Q.

What are pseudo forces? Explain using diagrams

Q.

A table with smooth horizontal surface is placed in a cabin which moves in a circle of a large radius R with $\omega$. A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the strings along the outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the masses as seen from the cabin.

1. R

2. 3R

3. 

4. 

Q.

A person stands on a spring balance at the equator. If the speed of earth's rotation increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case(approximately)?

1. 12 hr

2. 2 hr

3. 4 hr

4. 1 hr

Q. A balloon is massless when it is empty and its thickness is almost zero. The ballon is tightly inflated with air and left hanging in a car. The car starts moving ahead with acceleration 'a' then in the frame of the car(at equilibrium state)

1. The balloon will move backward
2. The ballon can move in any direction
3. The balloon will move forward
4. The balloon will be at the same position

Q. Two bodies of masses $4kg$ and $3kg$ respectively are connected by a light string passing over a smooth friction pulley. Calculate the acceleration of the masses and the tension in the string.

Q. In the figure, a smooth pulley of negligible weightis suspended by a spring balance. Weights of 1kg and 5kg are attached to the opposite ends ofa string passing over the pulley and move witha acceleration because of gravity. During theirmotion, the spring balcne reads a weight of

1. 1. 6 kg
2. Less than 6 kg
3. More than 6 kg
4. May be more or less than 6kg

Q.

$Abodyhangsfromaspringbalancesupportedfromthefromtheceilingofanelevator.Iftheelevatorhasanupwardaccelerationof2.5m/s^{2}andthebalancereads50N,whatisthetrueweightofthebody?$

1. (i) - p; (ii) - q; (iii) - r

2. 

3. 

4. 

Q. A person of mass $60kg$ is inside a lift of mass $940kg$ and he presses the button on the control panel. The lift starts moving upwards with an acceleration of $1{m/s}^2$. If $g=10{m/s}^2$, the tension in the supporting cable is

1. $8600\text{N}$
2. $9680\text{N}$
3. $11000\text{N}$
4. $1200\text{N}$

Q. A body of mass 5kg is suspended by a spring balance on an inclined plane as shown. The spring balance measures.

1. 5 N
2. 25 N
3. 50 N
4. 75 N

Q. An $80kg$ man stands on a spring balance in an elevator. When it start to move, the scale reads $700N$. What is the acceleration of the elevator? $(g=10{ms}^{-2})$

Q. The mass of a lift $600kg$ and it is moving upward with a uniform acceleration of $2m/s^2$.Then the tension in the cable of the lift is-

1. 7200 N
2. 5880 N
3. 4680 N
4. Zero N

Q.

A table with smooth horizontal surface is placed in a cabin which moves in a circle of a large radius R with $\omega$. A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the strings along the outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the masses as seen from the cabin.

1. ${\omega }^2$R

2. 3${\omega }^2$R

3. $\frac{{\omega }^{2}R}{3}$

4. $\frac{{\omega }^2}{R}$

Q. A balloon is massless when it is empty and its thickness is almost zero. The ballon is tightly inflated with air and left hanging in a car. The car starts moving ahead with acceleration 'a' then in the frame of the car(at equilibrium state)

1. The balloon will move forward
2. The balloon will move backward
3. The ballon can move in any direction
4. The balloon will be at the same position

Q. A person of mass $60kg$ is inside a lift of mass $940kg$ and he presses the button on the control panel. The lift starts moving upwards with an acceleration of $1{m/s}^2$. If $g=10{m/s}^2$, the tension in the supporting cable is

1. $8600\text{N}$
2. $9680\text{N}$
3. $11000\text{N}$
4. $1200\text{N}$

Q. A raw egg and hard boiled are made to spin on a a table with the same angular speed about the same axis. The ratio of the time taken by the two to stop is

1. Equal to one
2. Less then one
3. more than one
4. Equal to two

Q.

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of $5m/s^2$, the reading of the spring balance will be:

1. 49 N
2. 24 N
3. 74 N
4. 15 N

Q. A balloon is massless when it is empty and its thickness is almost zero. The ballon is tightly inflated with air and left hanging in a car. The car starts moving ahead with acceleration 'a' then in the frame of the car(at equilibrium state)

1. The balloon will move forward
2. The balloon will move backward
3. The balloon will be at the same position
4. The ballon can move in any direction

Q. a railway of mass $50$ tons is pulling a wagon of mass $40$ tons with a force of $4500N$ . The resistance force acting is $1N$ per ton. The tension in the coupling between the engine and the wagon is :

1. $1600N$
2. $2000N$
3. $3000N$
4. $1500N$

Q. The mass of an elevator is $4000$kg. Starting from rest how much distance with it rise in $3$s. If the tension in the cable is $48$kN?

1. $3m$
2. $4m$
3. $10m$
4. $16m$

Q. Determine the acceleration of the masses w.r.t. lift and tension in the string if the whole system in moving vertically upwards with uniform acceleration $a_0$. $(m_1>m_2)$

Q. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the balance reads $49\text{N}$, when the lift is stationary. If the lift moves downward with an acceleration of $5{\text{m/s}}^2$, the reading of the spring balance would be

1. $24\text{N}$
2. $15\text{N}$
3. $49\text{N}$
4. $74\text{N}$

Q. A cat lunges towards its unsuspecting owner. Treat the cat as a point mass of mass $m=2kg$ and the owner as a stationary point mass of mass $M=60kg$ located at $y=0m$.
If the cat has velocity $v_0=0m/s$ at height $y_0=2.0m$ at $t=0sec$, when will the cat-owner system have a center-of-mass height of $y_{CM}=0.01m$?

1. Never
2. $t=0.0sec$
3. $t=0.42sec$
4. $t=0.64sec$
5. $t=0.59sec$

Q. An object is weighed at the North pole by a beam balance and a spring balance, giving readings of $W_B$ and $W_S$ respectively. It is again weighed in the same manner at the equator, giving readings of $W_B^{\prime }$ and $W_S^{\prime }$ respectively. Assume that the acceleration due to gravity is the same everywhere and that the balances are quite sensitive.

1. $W_B=W_S$
2. $W_B=W_B^{\prime }$
3. $W_B^{\prime }=W_S^{\prime }$
4. $W_S^{\prime }=W_S$

Q. A man weighing 60 kg stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude 0.1 m and frequency $2/\pi$ Hz. Which of the following statements is correct?

1. The spring balance reads the weight of man as 60kg
2. The spring balance reading fluctuates between 60 kg. and 70 kg
3. The spring balance reading fluctuates between 50 kg and 60 kg
4. The spring balance reading fluctuates between 50 kg and 70 kg

Q. From a fixed pulley the masses $2\text{kg}$, $1\text{kg}$ and $3\text{kg}$ are suspended as shown in the figure. Find the extension in spring if its stiffness is $k=100\text{N/m}$. Assume the acceleration of $1\text{kg}$ and $3\text{kg}$ to be same.
(Take $g=10{\text{m/s}}^2$)

1. $0.5\text{m}$
2. $0.4\text{m}$
3. $0.2\text{m}$
4. $0.3\text{m}$