A block of mass 1 kg and density 0.8 g/cm^3 is held stationary with the help of a string as shown in figure. The block is completely immersed into the water filled in tank.If the tank is accelerating vertically upwards with an acceleration a = 2 m/s^2.

(i) Find the tension in the string.

A block of mass 1 kg and density 0.8 <span class="wp-katex-eq" data-display="false">g/cm^3</span> is held stationary with the help of a string as shown in figure. The block is completely immersed into the water filled in tank.If the tank is accelerating vertically upwards with an acceleration a = 2<span class="wp-katex-eq" data-display="false">m/s^2</span>. Find the tension in the string.

(A) 3 N

(B) 2 N

(C) 3.5 N

(D) 5.5 N

Solution

Let V = Volume of body

\rho = density of block = 0.8 \frac{g}{cm^3}=800\frac{kg}{m^3}

\sigma = density of water =1000\frac{kg}{m^3}

We know that, the mass of block= m=\;\rho\;V

\rho=\frac mV

V=\frac m\rho

We know that F_{up}=V\sigma(g+a)\;

\Rightarrow F_{up}=\frac m\rho\sigma(g+a)\;

\Rightarrow F_{up}=\frac1{800}\ast1000\ast(10+2)=15N

According to Newton's 2nd law of motion, we can write

F_{net}= F_{up}-T- mg

ma= F_{up} -T- mg

1*2= 15-T-1*10

2= 15 - T- 10

T= 15 - 10-2=3N

(A) is correct option

(ii) Determine the acceleration produced in the of block when the string is cut off.

(A) 3 ms^{-2} downwards

(B) 3 ms^{-2} upwards

(C) 2 ms^{-2} upwards

(D) 5 ms^{-2} upwards

When string is cut off then T=0 and the block will move upwards due to upwards force as density of block is lesser than that of water.

We know that, the acceleration = a^{'}=\frac{F_{net}}m

a^{'}=\frac{F_{up}-mg}m=\;\frac{15-1\ast10}1=\frac{15-10}1=5\;ms^{-2}

(D) is correct option

A block of mass 1 kg and density 0.8 <span class="wp-katex-eq" data-display="false">g/cm^3</span> is held stationary with the help of a string as shown in figure. The block is completely immersed into the water filled in tank.If the tank is accelerating vertically upwards with an acceleration a = 2 <span class="wp-katex-eq" data-display="false">m/s^2.</span>

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