Gravtiational PE
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Two masses M and m (with M > m) are connected by means of a pulley as shown in the figure. The system is released from rest. At the instant when mass M has fallen through a distance h, the velocity of mass m will be
√2gh
√2ghMm
√2gh(M−m)(M+m)
√2gh(M+m)(M−m)
If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is
12mgR
2 mgR
mgR
14mgR
- 700 J
- 7000 J
- 500 J
- 5000 J
Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kgm−1. The work done in lifting water to the ground from the surface of water in the well 20 m below is [g = 10 ms−2]
1.4×104J
1.5×104J
9.8×106J
18 J
A uniform chain of mass M and length L is held on a horizontal frictionless table with 1nth of its length hanging over the edge of the table. The work done is pulling the chain up on the table is
MgLn
MgL2n
MgLn2
MgL2n2
- Mass of the book and time taken
- Weight of the book and height of the book shelf
- Height of the book shelf and time taken
- Mass of the book, height of the book shelf and time taken.
- 10 J
- 5 J
- 2.5 J
- 1.25 J
A body of mass m = 1 kg is dropped from a height h = 40 cm on a horizontal platform fixed to one end of an elastic spring, the other being fixed to a base as shown in the figure. As a result, the spring is compressed by an amount x = 10 cm. What is the force constant of the spring? Take g=10 ms−2.
600 Nm−1
800 Nm−1
1000 Nm−1
1200 Nm−1
- 48 J
- 124 J
- 96 J
- 132 J
If ω1, ω2 and ω3 represent the work done in moving a particle from A to B along three different paths 1, 2, and 3 respectively in the presence of a gravitational field, then find the correct relation between ω1, ω2 and ω3.
ω1>ω2>ω3
ω1<ω2<ω3
ω1=ω2=ω3
None of these
- 2
- 1
- 12
- 34
P→Solid sphere, Q→Solid cube, R→Solid cone, S→Solid cylinder
Assuming potential energy ′U′ at the ground level to be zero.
All objects are made of the same material.
UP=Potential energy of solid sphere
UQ=Potential energy of solid cube
UR=Potential energy of solid cone
US=Potential energy of solid cylinder
Identify the correct option(s).
- US>UP
- UQ>US
- UP>UQ
- UP>US
- mgl2
- 2mgl5
- mgl5
- 4mgl5
- 2
- 1
- 12
- 34
A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is?
√u2−2gL
√2gL
√u2−gL
√2(u2−gL)
A mass M is lowered with the help of a string by a distance h at a constant acceleration g2. The work done by string will be
Mgh2
−Mgh2
3Mgh2
−3Mgh2
- 21g2
- 9g2
- 12g
- 6g
Two masses M and m (with M > m) are connected by means of a pulley as shown in the figure. The system is released from rest. At the instant when mass M has fallen through a distance h, the velocity of mass m will be
√2gh
√2ghMm
√2gh(M−m)(M+m)
√2gh(M+m)(M−m)
- 10 J
- 5 J
- 2.5 J
- 1.25 J