Question

coordinates \( (0,6) \mathrm{m} \) ? 2. A door 1 m wide and of mass 15 kg , is hinged at one side so that it can rotate without friction about a vertical axis. The door is initially unlatched. A bullet of mass 10 grams travelling at \( 400 \mathrm{~m} / \mathrm{s} \) lodges exactly into the centre of the door in a direction perpendicular to the plane of the door. Find the angular speed of the door just after the bullet embeds itself in the door. Is kinetic energy conserved? 3. A conical pendulum consists of a bob of mass \( m \) in motion in a circular path as shown in figure 3.1. Fig. 3.1 During the motion, the supporting wire of length \( l \) maintains the constant angle \( \theta \) with the vertical. Show that the magnitude of the angular momentum of the bob about the centre of the circle is 1 \[ L=\left(\frac{m^{2} g l^{3} \sin ^{4} \theta}{\cos \theta}\right)^{\frac{1}{2}} \] 4. (a) A system consists of particles of masses 5,2 and 3 grams located at ( \( 1,0,-1 \) ), ( \( 1,2,1 \) ) and ( \( 1,1,-3 \) ), respectively. Find the position of centre of mass of the system of narticles. (b) Locate the centre of mass of a system of particles of masses \( m_{1}=1 \) \( m_{3}=3 \mathrm{~kg} \), situated at the corners of an equilateral triangle of side 10 cr 5. Calculate the centre of mass of a non-uniform rod whose mass per un \( \rho=\rho_{o} \frac{x^{2}}{L} \), where \( \rho_{o} \) is a constant, \( L \) is the length of the rod and any point on the rod measured from one end.

          coordinates \( (0,6) \mathrm{m} \) ?
2. A door 1 m wide and of mass 15 kg , is hinged at one side so that it can rotate without friction about a vertical axis. The door is initially unlatched. A bullet of mass 10 grams travelling at \( 400 \mathrm{~m} / \mathrm{s} \) lodges exactly into the centre of the door in a direction perpendicular to the plane of the door. Find the angular speed of the door just after the bullet embeds itself in the door. Is kinetic energy conserved?
3. A conical pendulum consists of a bob of mass \( m \) in motion in a circular path as shown in figure 3.1.

Fig. 3.1
During the motion, the supporting wire of length \( l \) maintains the constant angle \( \theta \) with the vertical. Show that the magnitude of the angular momentum of the bob about the centre of the circle is
1
\[
L=\left(\frac{m^{2} g l^{3} \sin ^{4} \theta}{\cos \theta}\right)^{\frac{1}{2}}
\]
4. (a) A system consists of particles of masses 5,2 and 3 grams located at ( \( 1,0,-1 \) ), ( \( 1,2,1 \) ) and ( \( 1,1,-3 \) ), respectively. Find the position of centre of mass of the system of narticles. (b) Locate the centre of mass of a system of particles of masses \( m_{1}=1 \) \( m_{3}=3 \mathrm{~kg} \), situated at the corners of an equilateral triangle of side 10 cr
5. Calculate the centre of mass of a non-uniform rod whose mass per un \( \rho=\rho_{o} \frac{x^{2}}{L} \), where \( \rho_{o} \) is a constant, \( L \) is the length of the rod and any point on the rod measured from one end.

coordinates (0,6) m ?
2. A door 1 m wide and of mass 15 kg , is hinged at one side so that it can rotate without friction about a vertical axis. The door is initially unlatched. A bullet of mass 10 grams travelling at 400 m / s lodges exactly into the centre of the door in a direction perpendicular to the plane of the door. Find the angular speed of the door just after the bullet embeds itself in the door. Is kinetic energy conserved?
3. A conical pendulum consists of a bob of mass m in motion in a circular path as shown in figure 3.1.

Fig. 3.1
During the motion, the supporting wire of length l maintains the constant angle θ with the vertical. Show that the magnitude of the angular momentum of the bob about the centre of the circle is
1

L=((m^2 g l^3sin ^4θ)/(cosθ))^(1)/(2)

4. (a) A system consists of particles of masses 5,2 and 3 grams located at ( 1,0,-1 ), ( 1,2,1 ) and ( 1,1,-3 ), respectively. Find the position of centre of mass of the system of narticles. (b) Locate the centre of mass of a system of particles of masses m1=1 m3=3 kg, situated at the corners of an equilateral triangle of side 10 cr
5. Calculate the centre of mass of a non-uniform rod whose mass per un ρ=ρo(x^2)/(L), where ρo is a constant, L is the length of the rod and any point on the rod measured from one end.

Added by Stephen C.

Question

Please give Ace some feedback