355830
A force \(F=A y^{2}+B y+C\) acts on a body in the \(y\)-direction. The work done by this force during a displacement from \(y=-a\) to \(y=a\) is
1 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
2 \(\dfrac{2 A a^{3}}{3}+2 C a\)
3 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
4 None of these
Explanation:
\(\begin{aligned}& W=\int F_{y} d y=\int_{-a}^{a}\left(A y^{2}+B y+C\right) d y \\& =A\left[\dfrac{y^{3}}{3}\right]_{-a}^{a}+B\left[\dfrac{y^{2}}{2}\right]_{-a}^{a}+C[y]_{-a}^{a} \\& W=\dfrac{2 A a^{3}}{3}+2 C a\end{aligned}\)
PHXI06:WORK ENERGY AND POWER
355831
A position dependent force \(F=7-2 x+3 x^{2}\) newton acts on a small body of mass 2 \(kg\) and displace it from \(x=0\) to \(x=5 m\). The work done in joules is
1 135
2 35
3 270
4 70
Explanation:
\(\begin{gathered}W=\int_{0}^{5} F d x=\int_{0}^{5}\left(7-2 x+3 x^{2}\right) d x=\left[7 x-x^{2}+x^{3}\right]_{0}^{5} \\W=135 J\end{gathered}\)
PHXI06:WORK ENERGY AND POWER
355832
A body of mass 200 g is moving along \({x-y}\) plane. Work done by the force \({\vec{F}=(2 x \hat{i}+y \hat{j})}\), when it displaces a body \({(0,0)}\) to \({(1,2)}\) is
1 3 units
2 6 units
3 5 units
4 1.5 units
Explanation:
\(W=\int_{(0,0)}^{(1,2)}(2 x \hat{i}+y \hat{j}) \cdot(d x \hat{i}+d y \hat{j})\) \({\left[\because W=\int_{x_{1}}^{x_{2}} F . d s\right]}\) \({\int_{0}^{1} 2 x d x+\int_{0}^{2} y d y}\) \({=\left[2 \dfrac{x^{2}}{2}\right]+\left[\dfrac{y^{2}}{2}\right]=3}\) units
PHXI06:WORK ENERGY AND POWER
355833
A force \(F\) acting on an object varies with distance \(x\) as shown here. The force is in \(N\) and \(x\) in \(m\). The work done by the force in moving the object from \(x=0\) to \(x = 6\;m\) is
1 \(18.0\,J\)
2 \(13.5\;J\)
3 \(9.0\,J\)
4 \(4.5\,J\)
Explanation:
Work done \(=\) area under \(F-x\) graph \(=\) area of trapezium \(OABC = \frac{1}{2}(3 + 6)(3) = 13.5\;J\)
355830
A force \(F=A y^{2}+B y+C\) acts on a body in the \(y\)-direction. The work done by this force during a displacement from \(y=-a\) to \(y=a\) is
1 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
2 \(\dfrac{2 A a^{3}}{3}+2 C a\)
3 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
4 None of these
Explanation:
\(\begin{aligned}& W=\int F_{y} d y=\int_{-a}^{a}\left(A y^{2}+B y+C\right) d y \\& =A\left[\dfrac{y^{3}}{3}\right]_{-a}^{a}+B\left[\dfrac{y^{2}}{2}\right]_{-a}^{a}+C[y]_{-a}^{a} \\& W=\dfrac{2 A a^{3}}{3}+2 C a\end{aligned}\)
PHXI06:WORK ENERGY AND POWER
355831
A position dependent force \(F=7-2 x+3 x^{2}\) newton acts on a small body of mass 2 \(kg\) and displace it from \(x=0\) to \(x=5 m\). The work done in joules is
1 135
2 35
3 270
4 70
Explanation:
\(\begin{gathered}W=\int_{0}^{5} F d x=\int_{0}^{5}\left(7-2 x+3 x^{2}\right) d x=\left[7 x-x^{2}+x^{3}\right]_{0}^{5} \\W=135 J\end{gathered}\)
PHXI06:WORK ENERGY AND POWER
355832
A body of mass 200 g is moving along \({x-y}\) plane. Work done by the force \({\vec{F}=(2 x \hat{i}+y \hat{j})}\), when it displaces a body \({(0,0)}\) to \({(1,2)}\) is
1 3 units
2 6 units
3 5 units
4 1.5 units
Explanation:
\(W=\int_{(0,0)}^{(1,2)}(2 x \hat{i}+y \hat{j}) \cdot(d x \hat{i}+d y \hat{j})\) \({\left[\because W=\int_{x_{1}}^{x_{2}} F . d s\right]}\) \({\int_{0}^{1} 2 x d x+\int_{0}^{2} y d y}\) \({=\left[2 \dfrac{x^{2}}{2}\right]+\left[\dfrac{y^{2}}{2}\right]=3}\) units
PHXI06:WORK ENERGY AND POWER
355833
A force \(F\) acting on an object varies with distance \(x\) as shown here. The force is in \(N\) and \(x\) in \(m\). The work done by the force in moving the object from \(x=0\) to \(x = 6\;m\) is
1 \(18.0\,J\)
2 \(13.5\;J\)
3 \(9.0\,J\)
4 \(4.5\,J\)
Explanation:
Work done \(=\) area under \(F-x\) graph \(=\) area of trapezium \(OABC = \frac{1}{2}(3 + 6)(3) = 13.5\;J\)
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI06:WORK ENERGY AND POWER
355830
A force \(F=A y^{2}+B y+C\) acts on a body in the \(y\)-direction. The work done by this force during a displacement from \(y=-a\) to \(y=a\) is
1 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
2 \(\dfrac{2 A a^{3}}{3}+2 C a\)
3 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
4 None of these
Explanation:
\(\begin{aligned}& W=\int F_{y} d y=\int_{-a}^{a}\left(A y^{2}+B y+C\right) d y \\& =A\left[\dfrac{y^{3}}{3}\right]_{-a}^{a}+B\left[\dfrac{y^{2}}{2}\right]_{-a}^{a}+C[y]_{-a}^{a} \\& W=\dfrac{2 A a^{3}}{3}+2 C a\end{aligned}\)
PHXI06:WORK ENERGY AND POWER
355831
A position dependent force \(F=7-2 x+3 x^{2}\) newton acts on a small body of mass 2 \(kg\) and displace it from \(x=0\) to \(x=5 m\). The work done in joules is
1 135
2 35
3 270
4 70
Explanation:
\(\begin{gathered}W=\int_{0}^{5} F d x=\int_{0}^{5}\left(7-2 x+3 x^{2}\right) d x=\left[7 x-x^{2}+x^{3}\right]_{0}^{5} \\W=135 J\end{gathered}\)
PHXI06:WORK ENERGY AND POWER
355832
A body of mass 200 g is moving along \({x-y}\) plane. Work done by the force \({\vec{F}=(2 x \hat{i}+y \hat{j})}\), when it displaces a body \({(0,0)}\) to \({(1,2)}\) is
1 3 units
2 6 units
3 5 units
4 1.5 units
Explanation:
\(W=\int_{(0,0)}^{(1,2)}(2 x \hat{i}+y \hat{j}) \cdot(d x \hat{i}+d y \hat{j})\) \({\left[\because W=\int_{x_{1}}^{x_{2}} F . d s\right]}\) \({\int_{0}^{1} 2 x d x+\int_{0}^{2} y d y}\) \({=\left[2 \dfrac{x^{2}}{2}\right]+\left[\dfrac{y^{2}}{2}\right]=3}\) units
PHXI06:WORK ENERGY AND POWER
355833
A force \(F\) acting on an object varies with distance \(x\) as shown here. The force is in \(N\) and \(x\) in \(m\). The work done by the force in moving the object from \(x=0\) to \(x = 6\;m\) is
1 \(18.0\,J\)
2 \(13.5\;J\)
3 \(9.0\,J\)
4 \(4.5\,J\)
Explanation:
Work done \(=\) area under \(F-x\) graph \(=\) area of trapezium \(OABC = \frac{1}{2}(3 + 6)(3) = 13.5\;J\)
355830
A force \(F=A y^{2}+B y+C\) acts on a body in the \(y\)-direction. The work done by this force during a displacement from \(y=-a\) to \(y=a\) is
1 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
2 \(\dfrac{2 A a^{3}}{3}+2 C a\)
3 \(\dfrac{2 A a^{5}}{3}+\dfrac{B a^{2}}{2}+C a\)
4 None of these
Explanation:
\(\begin{aligned}& W=\int F_{y} d y=\int_{-a}^{a}\left(A y^{2}+B y+C\right) d y \\& =A\left[\dfrac{y^{3}}{3}\right]_{-a}^{a}+B\left[\dfrac{y^{2}}{2}\right]_{-a}^{a}+C[y]_{-a}^{a} \\& W=\dfrac{2 A a^{3}}{3}+2 C a\end{aligned}\)
PHXI06:WORK ENERGY AND POWER
355831
A position dependent force \(F=7-2 x+3 x^{2}\) newton acts on a small body of mass 2 \(kg\) and displace it from \(x=0\) to \(x=5 m\). The work done in joules is
1 135
2 35
3 270
4 70
Explanation:
\(\begin{gathered}W=\int_{0}^{5} F d x=\int_{0}^{5}\left(7-2 x+3 x^{2}\right) d x=\left[7 x-x^{2}+x^{3}\right]_{0}^{5} \\W=135 J\end{gathered}\)
PHXI06:WORK ENERGY AND POWER
355832
A body of mass 200 g is moving along \({x-y}\) plane. Work done by the force \({\vec{F}=(2 x \hat{i}+y \hat{j})}\), when it displaces a body \({(0,0)}\) to \({(1,2)}\) is
1 3 units
2 6 units
3 5 units
4 1.5 units
Explanation:
\(W=\int_{(0,0)}^{(1,2)}(2 x \hat{i}+y \hat{j}) \cdot(d x \hat{i}+d y \hat{j})\) \({\left[\because W=\int_{x_{1}}^{x_{2}} F . d s\right]}\) \({\int_{0}^{1} 2 x d x+\int_{0}^{2} y d y}\) \({=\left[2 \dfrac{x^{2}}{2}\right]+\left[\dfrac{y^{2}}{2}\right]=3}\) units
PHXI06:WORK ENERGY AND POWER
355833
A force \(F\) acting on an object varies with distance \(x\) as shown here. The force is in \(N\) and \(x\) in \(m\). The work done by the force in moving the object from \(x=0\) to \(x = 6\;m\) is
1 \(18.0\,J\)
2 \(13.5\;J\)
3 \(9.0\,J\)
4 \(4.5\,J\)
Explanation:
Work done \(=\) area under \(F-x\) graph \(=\) area of trapezium \(OABC = \frac{1}{2}(3 + 6)(3) = 13.5\;J\)
