Number 12.33. 12.34Please help me 1233. A small sphere of mass m and radius r slides down

Number 12.33. 12.34Please help me

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1233. A small sphere of mass m and radius r slides down a smooth stationary large sphere of radius R under the action of gravity from a position of rest at the top. Use Lagrange's equations to find the reaction of the sphere on the particle at any value 6, 0 being the angle between the vertical diam- eter of the sphere and the normal to the sphere that passes through the particle. Find the value of o at which the particle falls off. 1234. A partick of mass m is constrained to move along a smooth wire bent into the form of a horizon- al circk of radius a. Initially, thc particle has a velocity vn. The motion is subject to air resistance proportional to the square of the velocity. Using Lagrange's method, find the angular poOsition of the particle as a function of time. Calculate the reaction of the wire on the particle. Ignore the ef- fect of gravity. 1233. A small sphere of mass m and radius r slides down a smooth stationary large sphere of radius R under the action of gravity from a position of rest at the top. Use Lagrange's equations to find the reaction of the sphere on the particle at any value 6, 0 being the angle between the vertical diam- eter of the sphere and the normal to the sphere that passes through the particle. Find the value of o at which the particle falls off. 1234. A partick of mass m is constrained to move along a smooth wire bent into the form of a horizon- al circk of radius a. Initially, thc particle has a velocity vn. The motion is subject to air resistance proportional to the square of the velocity. Using Lagrange's method, find the angular poOsition of the particle as a function of time. Calculate the reaction of the wire on the particle. Ignore the ef- fect of gravity.