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Surbhi Singh
Subject: Physics
, asked on 14/5/18
Please give a detailed solution
Q.
A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to free end of the string. The system is released from rest. The speed of the block as it descends though a height h, is
Answer
1
Surbhi Singh
Subject: Physics
, asked on 14/5/18
pls answer this wirh a detailed solution:
18.
A thin wire Of length l and mass m is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be
$\left(1\right){\mathrm{ml}}^{2}\left(2\right)\mathrm{Zero}\phantom{\rule{0ex}{0ex}}\left(3\right)\frac{{\mathrm{ml}}^{2}}{{\mathrm{\pi}}^{2}}\left(4\right)\frac{{\mathrm{ml}}^{2}}{2{\mathrm{\pi}}^{2}}$
Answer
1
Surbhi Singh
Subject: Physics
, asked on 14/5/18
four thin uniform rods each of length L and mass m are joined to form of a square . the moment of inertia of the square about an axis along its one diagonal is
Answer
1
Jeneeta Eliza John
Subject: Physics
, asked on 2/5/18
Explain qno.10 Ans(2)
Q.10. A force F is applied on a hollow sphere of mass M and radius R at a distance
$\frac{R}{3}$
from its centre of mass as shown in figure. If surface is rough then what will be the direction of rolling friction?
(1) Forward
(2) Backward
(3) First Forward then backward
(4) Rolling friction will not set
Answer
1
Jeneeta Eliza John
Subject: Physics
, asked on 2/5/18
8) A ring of mass M and radius R is rolling without slipping with angular velocity
$\omega $
on the horizontal plane as shown the figure. The magnitude al angular momentum of ring about the point of the contact of the ring. (Answer 2)
$\left(1\right)M{R}^{2}\omega \phantom{\rule{0ex}{0ex}}\left(2\right)2M{R}^{2}\omega \phantom{\rule{0ex}{0ex}}\left(3\right)\frac{1}{2}M{R}^{2}\omega \phantom{\rule{0ex}{0ex}}\left(4\right)Zero$
Answer
1
Jeneeta Eliza John
Subject: Physics
, asked on 2/5/18
Explain qno.2 .Ans(3):
2. Three identical rods each of mass
m
and length
l
form an equilateral triangle. Moment of inertia of the system about an axis as shown in figure will be.
$\left(1\right)\frac{3{\mathrm{ml}}^{2}}{2}\left(2\right)\frac{{\mathrm{ml}}^{2}}{2}\phantom{\rule{0ex}{0ex}}\left(3\right)\frac{{\mathrm{ml}}^{2}}{4}\left(4\right)\frac{2}{3}{\mathrm{ml}}^{2}$
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
Q 6
. Three identical rods, each of length l, are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is
$\left(A\right)\frac{l}{2}\left(B\right)\sqrt{\frac{3}{2}}l\left(C\right)\frac{l}{\sqrt{2}}\left(D\right)\frac{l}{\sqrt{3}}$
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
Solve this :
8.
A square plate of mass 10 kg and side 20 m is moving along the groove with the help of two ideal rollers (massless), connected at the corners A and B of the square, as shown in the figure. At a certain moment of time, during motion the corner A is moving with velocity 16 m/s downward. Find the speed of corner D.
(A) 32 m/s (B) 16 m/s
(C) 8 m/s (D) none
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
Solve this :
9. A uniform cylinder rolls from rest down the side of a trough given by y = x
^{2}
. The cylinder does not slip from A to B but the surface of the through is frictionless from B to C as shown. If the cylinder ascends up to C, then (Neglect the radius of cylinder).
$\left(\mathrm{a}\right){\mathrm{y}}_{2}={\mathrm{y}}_{1}\left(\mathrm{b}\right){\mathrm{y}}_{2}=\frac{2}{3}{\mathrm{y}}_{1}\phantom{\rule{0ex}{0ex}}\left(\mathrm{c}\right){\mathrm{y}}_{2}=\frac{{\mathrm{y}}_{1}}{3}\left(\mathrm{d}\right){\mathrm{y}}_{2}=\frac{2}{5}{\mathrm{y}}_{1}$
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
Solve this:
Q.15. A rod of mass m and length 2R can rotate about an axis passing through O in vertical plane. A disc of mass m and radius R is hinged to the other end P of the rod and can freely rotate about P. When disc is at lowest point both rod and disc has angular velocity
$\omega $
. If rod rotates by maximum angle
$\theta =60\xb0$
with downward vertical, then find
$\omega $
in terms of R and g. (all hinges are smooth)
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
Solve this:
Q.14. Three identical cylinders of radius R are in contact. Each cylinder is rotating with angular velocity
$\omega $
. A thin belt is moving without sliding on the cylinders. Calculate the magnitude of velocity of point P with respect to Q. P and Q are two points of belt which are in contact with the cylinder.
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
Solve this:
Q.13. A rod of length l is standing vertically frictionless surface. It is disturbed slightly from this position. Let
$\omega and\alpha $
be the angular speed and angular acceleration of the rod, when the rod turns through an angle
$\theta $
with the vertical, then find the value of acceleration of centre of mass of the rod.
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
12. Two thin planks are moving on a four identical cylinder as shown. There is no slipping at any contact points. Calculate the ratio of angular speed of upper cylinder to lower cylinder.
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
Plz don't give the link for the solution as solution provided is wrong and i would be glad if u help me in this!
Answer
1
Raj Aryan
Subject: Physics
, asked on 23/4/18
A and C are the correct answer. Pls explain how!
Q3. A uniform rod of length
$\mathcal{l}$
and mass 2m rests on a smooth horizontal table. A point of mass m moving horizontally at right angle to the rod with velocity v collides with one end of the rod and sticks to it, then:
(A) angular velocity of the system after collision is v/
$\mathcal{l}$
(B) angular velocity of the system after collision is v/ 2
$\mathcal{l}$
(C) the loss in kinetic energy of the system as a whole as a result of the collision is mv
^{2}
^{ }
/6
(D) the loss in Kinetic energy of the system as a whole as a result of the collision is 7mv
^{2}
/ 24
Answer
1
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Q.A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to free end of the string. The system is released from rest. The speed of the block as it descends though a height h, is18. A thin wire Of length l and mass m is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be

$\left(1\right){\mathrm{ml}}^{2}\left(2\right)\mathrm{Zero}\phantom{\rule{0ex}{0ex}}\left(3\right)\frac{{\mathrm{ml}}^{2}}{{\mathrm{\pi}}^{2}}\left(4\right)\frac{{\mathrm{ml}}^{2}}{2{\mathrm{\pi}}^{2}}$

Q.10. A force F is applied on a hollow sphere of mass M and radius R at a distance $\frac{R}{3}$ from its centre of mass as shown in figure. If surface is rough then what will be the direction of rolling friction?

(1) Forward

(2) Backward

(3) First Forward then backward

(4) Rolling friction will not set

$\left(1\right)M{R}^{2}\omega \phantom{\rule{0ex}{0ex}}\left(2\right)2M{R}^{2}\omega \phantom{\rule{0ex}{0ex}}\left(3\right)\frac{1}{2}M{R}^{2}\omega \phantom{\rule{0ex}{0ex}}\left(4\right)Zero$

2. Three identical rods each of mass

mand lengthlform an equilateral triangle. Moment of inertia of the system about an axis as shown in figure will be.$\left(1\right)\frac{3{\mathrm{ml}}^{2}}{2}\left(2\right)\frac{{\mathrm{ml}}^{2}}{2}\phantom{\rule{0ex}{0ex}}\left(3\right)\frac{{\mathrm{ml}}^{2}}{4}\left(4\right)\frac{2}{3}{\mathrm{ml}}^{2}$

Q 6. Three identical rods, each of length l, are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is$\left(A\right)\frac{l}{2}\left(B\right)\sqrt{\frac{3}{2}}l\left(C\right)\frac{l}{\sqrt{2}}\left(D\right)\frac{l}{\sqrt{3}}$

8.A square plate of mass 10 kg and side 20 m is moving along the groove with the help of two ideal rollers (massless), connected at the corners A and B of the square, as shown in the figure. At a certain moment of time, during motion the corner A is moving with velocity 16 m/s downward. Find the speed of corner D. (A) 32 m/s (B) 16 m/s(C) 8 m/s (D) none

Solve this :9. A uniform cylinder rolls from rest down the side of a trough given by y = x

^{2}. The cylinder does not slip from A to B but the surface of the through is frictionless from B to C as shown. If the cylinder ascends up to C, then (Neglect the radius of cylinder).$\left(\mathrm{a}\right){\mathrm{y}}_{2}={\mathrm{y}}_{1}\left(\mathrm{b}\right){\mathrm{y}}_{2}=\frac{2}{3}{\mathrm{y}}_{1}\phantom{\rule{0ex}{0ex}}\left(\mathrm{c}\right){\mathrm{y}}_{2}=\frac{{\mathrm{y}}_{1}}{3}\left(\mathrm{d}\right){\mathrm{y}}_{2}=\frac{2}{5}{\mathrm{y}}_{1}$

Q.15. A rod of mass m and length 2R can rotate about an axis passing through O in vertical plane. A disc of mass m and radius R is hinged to the other end P of the rod and can freely rotate about P. When disc is at lowest point both rod and disc has angular velocity $\omega $. If rod rotates by maximum angle $\theta =60\xb0$ with downward vertical, then find $\omega $ in terms of R and g. (all hinges are smooth)

Q.14. Three identical cylinders of radius R are in contact. Each cylinder is rotating with angular velocity $\omega $. A thin belt is moving without sliding on the cylinders. Calculate the magnitude of velocity of point P with respect to Q. P and Q are two points of belt which are in contact with the cylinder.

Q.13. A rod of length l is standing vertically frictionless surface. It is disturbed slightly from this position. Let $\omega and\alpha $ be the angular speed and angular acceleration of the rod, when the rod turns through an angle $\theta $ with the vertical, then find the value of acceleration of centre of mass of the rod.

Q3. A uniform rod of length $\mathcal{l}$ and mass 2m rests on a smooth horizontal table. A point of mass m moving horizontally at right angle to the rod with velocity v collides with one end of the rod and sticks to it, then:

(A) angular velocity of the system after collision is v/$\mathcal{l}$

(B) angular velocity of the system after collision is v/ 2$\mathcal{l}$

(C) the loss in kinetic energy of the system as a whole as a result of the collision is mv

^{2}^{ }/6(D) the loss in Kinetic energy of the system as a whole as a result of the collision is 7mv

^{2}/ 24