Question

Please help me with these physics practice questions thanks and God bless :(

Q16. Consider the box in the drawing. We can slide the box up the frictionless incline from point A and to point Cor we can slide it along the frictionless horizontal surface from point to point Band then lift it to point How does the work done on the box along path A-c to the work done on the box along the two step path A greater than WAc. A) WABc is much WAc B) WABc is slightly greater than D) WABC is slight less than WAC. E) The work done in both cases is the same. Q17. Two identical balls are thrown from the same height from the roof of a building, one ball is thrown upward with an initial speed v. The second ball is thrown downward with the same initial speed v. When the balls reach the ground, how do the kinetic energies of the two balls compare? Ignore any air resistance effects. A) The kinetic energies of the two balls will be the same B) The first ball will have twice the kinetic energy as the second ball. C The first ball will have one half the kinetic energy as the second ball. D) The first ball will have four times the kinetic energy as the second ball. E) The first ball will have three times the kinetic energy as the second ball. a Four objects start from rest and roll without slipping down The objects are a solid sphere, hollow solid cylinder, and a hollow sphere. Each of the objects has the same radius and the same mass, but they are made from different materials. Which object will have the greatest angular speed at the bottom of the ramp? A) Since they are all starting from rest, all of the objects will have the same speed at the bottom as a result of the conservation of mechanical energy. B) solid sphere CO hollow cylinder solid cylinder D) E) hollow sphere Q19. Two solid cylinders are rotating about an axis that passes through the center of both ends of each cylinder. cylinder A has three times the mass and twice the radius of cylinder B, but they have the same rotational kinetic energy. What is the ratio of the angular velocities, "Aleve for these two cylinders? B) 0.50 D) 2.0 E) 4.0 20. A solid sphere of radius R rotates about an axis that is tangent to the sphere with an angular speed co. Under the action of internal forces, the radius of the sphere increases to What is the final angular speed of the sphere? A) ex/4 B) co/2 D) 2w

Answer 1

Q16) E) work done in both the cases is same.

work done by all the forces is zero. and change in kinetic energy is zero.

then work done by external agent = - work done by gravity

Q17) A) the kinetic energies of two balls will be the same.

Q18) since they are starting from rest , all the objects will have the same kinetic energy at the bottom as a result of the conservation of mechanical energy. since the bodies are rolling $V=R\omega$

Kinetic energy at bottom is $\frac{1}{2}mV^2+\frac{1}{2}I\omega^2=mgh$

for solid sphere, $\frac{1}{2}mV^2+\frac{1}{2}\frac{2}{5}mR^2\omega^2=\frac{7mV^2}{10}=mgh$

speed at bottom is $V=\sqrt{\frac{10gh}{7}}$

for hollow cylinder, $\frac{1}{2}mV^2+\frac{1}{2}mR^2\omega^2=mV^2=mgh$

speed at bottom is $V=\sqrt{gh}$

for solid cylinder, $\frac{1}{2}mV^2+\frac{1}{2}\frac{1}{2}mR^2\omega^2=\frac{3mV^2}{4}=mgh$

speed at bottom is $V=\sqrt{\frac{4gh}{3}}$

for hollow sphere, $\frac{1}{2}mV^2+\frac{1}{2}\frac{2}{3}mR^2\omega^2=\frac{5mV^2}{6}=mgh$

speed at bottom is $V=\sqrt{\frac{6gh}{5}}$

since solid sphere has largest linear speed at bottom, It akso has largest angular speed at bottom.

Answer is B.

Q19) mass of A is m₁ = 3m

mass of B is m

radius of A is R₁ = 2R

radius of B is R

moment of inertia of a solid cylinder is $\frac{mR^2}{2}$

since A and B have same rotational kinetic energy

$\frac{I_1\omega_A^2}{2}=\frac{I_2\omega_B^2}{2}$

$\frac{3m(2R)^2\omega_A^2}{4}=\frac{mR^2\omega_B^2}{4}$

$\frac{\omega_A}{\omega_B}=0.28$

the closest answer is A

Q20)

Moment of inertia of solid sphere about tangential axis is $\frac{2}{5}MR^2+MR^2=\frac{7}{5}MR^2$ . As only internal forces are acting, angular momentum is conserved.

Initial angular momentum is $L_{i}=\frac{7}{5}MR^2\omega$

final angular momentum is $L_{f}=\frac{7}{5}M(2R)^2\omega'$

since $L_{i}=L_{f}$

$\frac{7}{5}MR^2\omega=\frac{7}{5}M(2R)^2\omega'$

$\omega'=\frac{\omega}{4}$

answer is A.