Acceleration Due To Gravity

Q.

A man of mass 70 kg stands on a weighing scale in a lift which is moving
a) upwards with a uniform speed of $10m{s}^{-1}$,
b) downwards with a uniform acceleration of $5m{s}^{-1}$,
c) upwards with a uniform acceleration of $5m{s}^{-1}$.
What would be the readings on the scale in each case?
d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

Q. A barometer kept in an elevator reads $76\text{cm}$ of mercury when the elevator is at rest. If the elevator goes upwards with some acceleration, the reading of the barometer will be

1. $76\text{cm}$
2. zero
3. $<76\text{cm}$
4. $>76\text{cm}$

Q. A liquid is filled in an open vessel and vessel is accelerated horizontally with a constant acceleration $a$. Choose the correct statements for the given situation.

1. The maximum pressure is at the leftmost bottom corner.
2. Along a horizontal line within the liquid, as we move from left to right, the pressure decreases
3. The pressure at all the points on a line making an angle of ${\tan }^{-1}\left(\frac{a}{g}\right)$ with horizontal would be same
4. Along a horizontal line within the liquid, as we move from left to right, the pressure remains the same

Q. A block of mass 2 kg, placed on a long frictionless horizontal table, is pulled horizontally by a constant force F. It is found to move 10 m in the first 2 s. Find the magnitude of the force F.

Q.

A U-tube containing a liquid is accelerated horizontally with a constant acceleration $a_0$. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.

Q.

A body is weighed by a spring balance to be 1.000 kg at the north pole. How much will it weigh at the equator ? Account for the earth's rotation only.

Q. A beaker containing a liquid of density $\rho$ moves up with an acceleration ${}^{\prime }{a}^{\prime }$. The pressure in the liquid at a depth $h$ below the free surface of the liquid is (consider atmospheric pressure to be $P_0$)

1. $P_0+h\rho g$
2. $P_0-h\rho (g-a)$
3. $P_0+h\rho (g+a)$
4. $P_0+2h\rho g\left(\frac{g+a}{g-a}\right)$

Q.

In figure $m_1=5$ kg and F = 1N. Find the acceleration of either block. Describe the motion of $m_1$ if the string breaks but F continues to act.

Q. A helicopter has a mass $m$ and maintains its height by imparting a downward momentum to a column of air defined by the slipstream boundary as shown in the figure. The propeller blades can project downward air at speed $v$, where the pressure in the stream below the blades is atmospheric and the radius of the circular cross section of the slip stream is $r$. Neglect any rotational energy of the air, the temperature rise due to air friction and any change in air density $\left(\rho \right)$. Then

1. $v=\frac{1}{r}\sqrt{\frac{mg}{\pi \rho }}$ for equilibrium
2. $v=\frac{2}{r}\sqrt{\frac{mg}{\pi \rho }}$ for equilibrium
3. Power of engine $\frac{mg}{2r}\sqrt{\frac{mg}{\pi \rho }}$ for equilibrium
4. Power of engine $\frac{mg}{r}\sqrt{\frac{mg}{\pi \rho }}$ for equilibrium

Q. When a dolphin glides through air, it experiences an external pressure of $0.75\text{m}$ of mercury. The absolute pressure on dolphin when it is $4\text{m}$ below the free surface of the water is
$[\text{Take}g=10{\text{m/s}}^2]$

1. $150\text{kPa}$
2. $135\text{kPa}$
3. $142\text{kPa}$
4. $40\text{kPa}$

Q. A tank is filled up to height $2H$ with a liquid and is placed on a platform of height $H$ from the ground. The distance $x$ from the ground is ${}^{\prime }{Z}^{\prime }H$ where a small hole is punched to get the maximum range $R$ then the value of ${}^{\prime }{Z}^{\prime }$ is

Q. An air bubble in a water tank rises from the bottom to the top. Which of the following statement(s) is/are true?

1. Bubble rises upwards because pressure at the bottom is less than that at the top
2. Bubble rises upwards because pressure at the bottom is greater than that at the top
3. As the bubble rises, its size increases
4. As the bubble rises, its size decreases

Q. if the rotational motion of earth increases, then the weight of the body-

1. will remain same
2. will increase
3. will decrease
4. none of these

Q. A beaker containing a liquid of density $\rho$ moves up with an acceleration a. The pressure due to the liquid at a depth h below the free surface of the liquid is

1. h $\rho$ (g-a)
2. 2h $\rho$g $\left(\frac{g+a}{g-a}\right)$
3. h $\rho$ g
4. h $\rho$ (g+a)

Q. A dynamometer $D$, is connected with two bodies of mass $M=6kg$ and $m=4kg$. If two forces $F=20N$ & $F=10N$ are applied on masses according to figure then reading of the dynamometer will be:

1. $10N$
2. $20N$
3. $14N$
4. $6N$

Q.

A boat is floating in water at 0${}^0$C such that 97% of the volume of the boat is submerged in water. The temperature at which the boat will just completely sink in water is $({\gamma }_R=3\times {10}^{-4}{/}^{o}C)$

1. ${10}^{0}C$
2. ${100}^{0}C$
3. ${60}^{0}C$
4. ${50}^{0}C$

Q.

Write mathematical form of Newton's second law of motion.

1. $F=m/g$
2. $F=ma$
3. $F=0$
4. $v=u+at$

Q.

The pressure at the bed of the ocean is $7.84\times {10}^{7}Pa.$Find the depth of the ocean. Density of water is ${10}^{3}kg{m}^{-3}$and $g=10m/s^2$

Q. A mercury barometer reads $75cm$ in a stationary lift. What reading does it show when the lift is moving downwards, with an acceleration of $1m/s^2$?

Q. Assertion :Surface tension has the same units as force gradient. Reason: Surface tension is the force gradient along the surface of liquid.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. If the centre of gravity of the body lies above the metacentre, then the body is said to be in ......................

1. stable equilibrium
2. unstable equilibrium
3. neutral equilibrium
4. Both (2) and (3)

Q. Consider a bent tube lowered slightly into a water stream as shown in figure. The velocity of stream relative to the tube is equal to $v=5{\text{ms}}^{-1}$. The closed upper end of the tube located at the height $h_0=10\text{cm}$ has a small orifice. The height ${}^{\prime }{h}^{\prime }$ to which water jet spurts (in $m$) is

Q. A beaker of liquid accelerates from rest, on a horizontal surface, with acceleration $a$ to the right.
How does the pressure vary with depth below the surface?

Q. A lift having a simple pendulum attached with its ceiling is moving upward with constant acceleration 'a'. What will be the tension in the string of pendulum with respect to a boy inside the lift and a boy standing on earth, mass of bob of simple pendulum is m.

Q. To measure atmospheric pressure, Torricelli in $1643$ made an instrument, which is called:

1. hygrometer
2. barometer
3. anemometer
4. none of these

Q. A barometer kept in an elevator reads $76\text{cm}$ of $Hg$. If the elevator starts accelerating upwards, then the height of the $Hg$ column in the barometer will be

1. $76\text{cm}$
2. less than $76\text{cm}$
3. greater than $76\text{cm}$
4. zero

Q. An air bubble in a water tank rises from the bottom to the top. Which of the following statement(s) is/are true?

1. Bubble rises upwards because pressure at the bottom is less than that at the top
2. Bubble rises upwards because pressure at the bottom is greater than that at the top
3. As the bubble rises, its size increases
4. As the bubble rises, its size decreases

Q. A body of mass m performs uniform circular motion along a circular path of radius $r$ with velocity $v$ . If its angular momentum is $L$ , then the centripetal force acting on it is:

1. $L^2/mr$
2. $L^2/m^3$
3. $L^2/m{r}^2$
4. $L^2/m{r}^3$

Q. A liquid is filled in an open vessel and vessel is accelerated horizontally with a constant acceleration $a$. Choose the correct statements for the given situation.

1. The maximum pressure is at the leftmost bottom corner.
2. Along a horizontal line within the liquid, as we move from left to right, the pressure decreases
3. The pressure at all the points on a line making an angle of ${\tan }^{-1}\left(\frac{a}{g}\right)$ with horizontal would be same
4. Along a horizontal line within the liquid, as we move from left to right, the pressure remains the same

Q. A liquid is filled in a container as shown in figure. Container is accelerated towards right. There are four points $A.B,C$ and $D$ in the liquid. Choose the correct options.

1. $P_A>P_B$
2. $P_C>P_A$
3. $P_D>P_B$
4. $P_A>P_C$