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The densitis of two solid spheres A and B of the same radii R very with radial distance raspA(r) = k (rR) and pB (r) = k (r(R)^5, respectively, where k is a constant . The moments of inertia of the inividual spheres about axes passing through their centres are IA and IB respectively. if IB /IA = n/10, the value of n is
02
Oct
The densitis of two solid spheres A and B of the same radii R very with radial distance raspA(r) = k (rR) and pB (r) = k (r(R)^5, respectively, where k is a constant . The moments of inertia of the inividual spheres about axes passing through their centres are IA and IB respectively. if [...]
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respectively ,
The densitis of two solid spheres A and B of the same radii R very with radial distance raspA(r) = k (rR) and pB (r) = k (r(R)^5 ,
the value of n is ,
where k is a constant . The moments of inertia of the inividual spheres about axes passing through their centres are IA and IB respectively. if IB /IA = n/10 ,
Two identical uniform discs roll without slipping on two different surfaces AB and CD starting at A and C with linear speed υ 1 and υ 2 , respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and υ 1 = 3 m/s then υ 2 in m/s is ( g = 10 m/s^2 )
02
Oct
Two identical uniform discs roll without slipping on two different surfaces AB and CD starting at A and C with linear speed υ 1 and υ 2 , respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and υ 1 = 3 [...]
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and always remain in contact with the surfaces. If they reach B and D with the same linear speed and υ 1 = 3 m/s then υ 2 in m/s is ( g = 10 m/s^2 ) ,
respectively ,
Two identical uniform discs roll without slipping on two different surfaces AB and CD starting at A and C with linear speed υ 1 and υ 2 ,
A horizontal circular platform of radius 0.5 m and mass axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 m/s with respect to the ground. The rotational speed of the platform in rad/s after the balls leace the platform is
02
Oct
A horizontal circular platform of radius 0.5 m and mass axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular [...]
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A horizontal circular platform of radius 0.5 m and mass axis. Two massless spring toy-guns ,
A particle of mass m is moving along the side of a square of side 'a' ,
with a uniform speed v in the x-y plane as shown in the figure. Which of the following statements is false for the angular momentum L about the origin? ,
In the List-I below, four different paths of a particle are given as functions of time. In these functions, and are positive constants of appropriate dimensions and . In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: is the linear momentum, is the angular momentum about the origin, is the kinetic energy, is the potential energy and is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.
02
Oct
In the List-I below, four different paths of a particle are given as functions of time. In these functions, and are positive constants of appropriate dimensions and . In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: is the linear [...]
A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque τ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?
02
Oct
A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque τ about an axis normal to [...]
Two thin circular discs of mass m and 4 m, having radii of a and 2 a, respectively, are rigidly fixed by a massless, rigid rod of length l = root 24 a through their centres. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is ω. The angular momentum of the entire assembly about the point ‘O’ is L → (see the figure). Which of the following statement(s) is(are) true?
02
Oct
Two thin circular discs of mass m and 4 m, having radii of a and 2 a, respectively, are rigidly fixed by a massless, rigid rod of length l = root 24 a through their centres. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so [...]
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A particle of mass m is moving along the side of a square of side 'a' ,
are rigidly fixed by a massless ,
having radii of a and 2 a ,
respectively ,
rigid rod of length l = root 24 a through their centres. This assembly is laid on a firm and flat surface ,
Two thin circular discs of mass m and 4 m ,
with a uniform speed v in the x-y plane as shown in the figure. Which of the following statements is false for the angular momentum L about the origin? ,
The position vector r→ of a particle of mass m is given by the following equation r→(t) = αt3 iˆ+β2 jˆ, where α = 10/3 m/s^3, β = 5 m/s^2 and m = 0.1 kg. At t = 1 s, which of the following statement (s) is (are) true about the particle?
02
Oct
The position vector r→ of a particle of mass m is given by the following equation r→(t) = αt3 iˆ+β2 jˆ, where α = 10/3 m/s^3, β = 5 m/s^2 and m = 0.1 kg. At t = 1 s, which of the following statement (s) is (are) true about the particle? The position vector [...]
A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision:
02
Oct
A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. [...]
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A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1m/s. A small ball of mass 0.1 kg ,
hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision: ,
moving with velocity 20 m/s in the opposite direction ,
The potential energy of a particle of mass m at a distance r from a fixed point O is given by V(r)=kr 2 /2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If v is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true ?
02
Oct
The potential energy of a particle of mass m at a distance r from a fixed point O is given by V(r)=kr 2 /2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If v is the speed of the [...]
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A particle of mass m is moving along the side of a square of side 'a' ,
The potential energy of a particle of mass m at a distance r from a fixed point O is given by V(r)=kr 2 /2 ,
with a uniform speed v in the x-y plane as shown in the figure. Which of the following statements is false for the angular momentum L about the origin? ,
A ring of mass M and radius R is rotating with angular speed ω about a fixed vertical axis passing through its centre O with two point masses each of mass M/8 at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is 8/9 ω and one for the masses is at a distance of 3/5 R from O. At this instant the distance of the other mass from O is
02
Oct
A ring of mass M and radius R is rotating with angular speed ω about a fixed vertical axis passing through its centre O with two point masses each of mass M/8 at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. [...]