The bob of a pendulum is released from a horizontal position. If the length of the pendulum is $1.5 \; m$,what is the speed (in $m/s$) with which the bob arrives at the lowermost point,given that it dissipated $5 \%$ of its initial energy against air resistance?

$A$ constant force of $5 N$ accelerates a stationary particle of mass $500 g$ through a displacement of $5 m$. The average power delivered is: (in $W$)

$A$ lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it,the initial speed of the bullet is ............ $m \, s^{-1}$.
(Given: Initial temperature of the bullet $= 127^{\circ} C$,
Melting point of the bullet $= 327^{\circ} C$,
Latent heat of fusion of lead $= 2.5 \times 10^{4} \, J \, kg^{-1}$,
Specific heat capacity of lead $= 125 \, J \, kg^{-1} K^{-1}$)

Two bodies have kinetic energies in the ratio $16: 9$. If they have the same linear momentum,the ratio of their masses respectively is

$A$ bullet of mass $30 \,g$ moving with $700 \,ms^{-1}$ collides with a block of mass $4 \,kg$ hanging by a string of length $0.4 \,m$. After the collision, the block rises to a height of $0.2 \,m$. Find the velocity of the bullet when it emerges from the block. (in $\,ms^{-1}$)

$A$ spherical bowl of radius $R = 2 \ m$ is placed on a horizontal plane. $A$ particle of mass $m = 1 \ g$ oscillates on its inner surface. If the particle starts from a point on the bowl at a height of $h = 1 \ cm$ from the horizontal plane and the coefficient of friction is $\mu = 0.01$,find the total distance $s$ traveled by the particle before it comes to rest at the bottom of the bowl. (in $m$)