Gravity

Q.

Marisol pushes a $3.0\text{kg}$ box $7.0\text{m}$ across the floor with a force of $12\text{N}$.

She lifts the box to a shelf $1\text{m}$ above the ground.

How much work does Marisol do on the box?

Q. A heavy particle is suspended by a string of length $l$. The particle is given a horizontal velocity $v_0$. The string becomes slack at some angle and the particle proceeds on a parabola. Find the value of $v_0$ if the particle passes through the point of suspension.

1. $v_0=\sqrt{gl[2+\sqrt{3}]}$
2. $v_0=\sqrt{gl}$
3. $v_0=\sqrt{gl[5+\sqrt{3}]}$
4. $v_0=\sqrt{gl\left[\frac{3+\sqrt{3}}{2}\right]}$

Q. A chain of length L is released from rest, from a frictionless surface with half length hanging as shown in figure. Work done by gravity when the chain is just completely off the surface.
(m=10 kg, g=10 $m/s^2$ and L=10 $m$)

1. 475 J
2. 375 J
3. 75 J
4. 250 J

Q. If A having a mass of 50 kg and B having the mass of 60 then B will attract A?

Q. An object of mass 5 kg falls from rest through a vertical distance of 20 m. and attains a velocity of 10 m/s. How much work is done by the resistance of the air on the object? $(g=10m/s^2)$

1. $-550J$
2. $-750J$
3. $-850J$
4. $-450J$

Q. In the arrangement shown in figure the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

1. 
2. 
3. 
4. 

Q. A uniform chain has a mass $m$ and length $l$. It is held on a frictionless table with two third of its length hanging over the edge. Find the work done in just pulling the hanging part back on the table.

Q. A chain of length L is released from rest, from a frictionless surface with half length hanging as shown in figure. Work done by gravity when the chain is just completely off the surface.
(m=10 kg, g=10 $m/s^2$ and L=10 $m$)

1. 475 J
2. 375 J
3. 250 J
4. 75 J

Q.

A person of mass $M$ is sitting on a swing of length $L$ and swinging with an angular amplitude ${\theta }_0$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $\ell (\ell <<L)$, is close to :

1. $Mg\ell$
2. $Mg\ell (1+{\theta }_0^2)$
   
3. $Mg\ell (1-{\theta }_0^2)$
4. $Mg\ell (1+\frac{{\theta }_0^2}{2})$

Q. A body of mass $2kg$ is thrown up with a speed of $25m/s$. Find is max potential energy

Q. A wire suspended vertically from one of its ends is stretched by attaching a weight of $200N$ to the lower end. The weight stretched the wire by $1mm$. Then the elastic energy stored in the wire is (in J)

1. $0.1$
   
2. $0.2$
   
3. $10$
   
4. $20$
   

Q. When a body of mass m is suspended from a spiral spring of natural length L, the spring gets stretched through a distance h. The potential energy of the stretched spring is-

1. $\frac{mg{h}^2}{2}$
2. $\frac{1}{2}mgh$
3. mgh
4. $\frac{1}{2}mg(L+h)$

Q. A chain of mass M and length L is kept on a table with $L/4$ portion overhanging from edge. Work done by external force to put the hanging portion back on the table:

1. $\frac{MgL}{32}$
2. $\frac{MgL}{8}$
3. $\frac{MgL}{16}$
4. $\frac{MgL}{12}$

Q. What will be the effect of gravity when two objects come closer to each other.

Q. A bicycle chain of length $1.6m$ and of mass $1kg$ is lying on a horizontal floor. The work done in lifting it with one end touching the floor and the other end $1.6m$ above the floor is (Take $g=10m{s}^{-2}$):

1. $3.2J$
2. $10J$
3. $8J$
4. $16J$